KeyTrain Applied Mathematics

Level 6 Introduction

For

Applied Mathematics Level 6 Published by SAI Interactive, Inc., 340 Frazier Avenue, Chattanooga, TN 37405. Copyright © 2000 by SAI Interactive, Inc. KeyTrain is a registered trademark of SAI Interactive, Inc. WorkKeys is a registered trademark of ACT, Inc., used by permission. This document may contain material from or derived from ACT’s Targets for Instruction, copyright ACT, Inc., used by permission. Portions copyright Advancing Employee Systems, Inc., used by permission.

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Page 1

KeyTrain Applied Mathematics

Level 6 Introduction

Level 6 Applied Mathematics Introduction Welcome to Level 6 of Applied Mathematics. At Level 6 the tasks are more complex. Problems will require several steps and calculations to solve. The wording and organization of the problems may also be more difficult. Although the problems are more difficult than in previous levels, the math involved is not. The key to understand these new problems is to see them as a series of smaller, easier problems. By breaking larger problems down into smaller ones, you will be able to solve these also.

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Page 2

KeyTrain Applied Mathematics

Level 6 Introduction

The Problems Will Include: - Solving complicated multiple-step problems that may require manipulation of the original information - Calculations using negative numbers, fractions, ratios, percentages and mixed numbers - Calculating multiple rates and then compare the ratios or use them to perform other calculations - Finding areas of rectangles and volumes of rectangular solids - Determining the best deal using the result in another problem, and - Finding mistakes in calculations.

Types of Numbers and Quantities The problems in this level deal with the same types of numbers and quantities you have used before: fractions, decimals, percentages and common units of measurement ( for weight, length, time, volume and temperature). You will also work with mixed units of measurement. You may have to convert units in order to solve other problems. In addition, you will also learn to find the area and volume of basic shapes using a formula. You may have to rearrange the formula to solve for the size of the shape from the area or volume.

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Page 3

KeyTrain Applied Mathematics

Level 6 Introduction

This Level Is Divided Into Seven Lessons: • Problem Solving Techniques • Multiple Step Problems • Fractions and Decimals • Percentages • Area and Volume • Rates, and • Best Deals.

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Page 4

KeyTrain Applied Mathematics

Level 6 Problem Solving

Level 6 Applied Mathematics Problem Solving There are many different techniques that can be used to solve problems. Sometimes there may be more than one way to solve a problem. In these cases there may be no right or wrong method to use. Some of these problem-solving methods are especially useful when the problems are more difficult. If several steps are involved, or the equations are very difficult, there may be an easier way to figure out the answer. This section will review some of these methods. Copyright © 2000, SAI Interactive, Inc. For use only by Chicago Public Schools.

Page 5

KeyTrain Applied Mathematics

Level 6 Problem Solving

Problem Solving Strategies Some of the problem solving strategies you can use are: • Making a Drawing or Diagram • Guessing and Testing • Working Backwards • Solving a Similar but Simpler Problem Examples of each of these methods will be shown. In all cases, it is not how you get the answer that is important. The important thing is if the answer is right. You can and should check your answer to be sure.

Making a Drawing or Diagram If the solution to a problem is not immediately obvious, then a drawing or diagram may help. This is most helpful if you can picture the problem in your mind, but you don't know how to write an equation for the problem. The drawing or diagram helps you to organize information and solve the problem. 1 $4

2 $8

3 $12

4 $16

5 $25

You can use charts or tables. or You can draw a diagram.

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Page 6

KeyTrain Applied Mathematics

Level 6 Problem Solving

Using a Chart to Solve a Problem Here is an example of using a diagram or chart to solve a problem:

There are two jobs you can apply for. The first job pays $22,000 the first year, with raises of $4,000 each year after. The second job pays $26,000 the first year with raises of $2,000 each year after. When would you make as much money in the first job as in the second?

The facts and the question are fairly easy to understand. But it is not so easy to see how to write an equation to solve the problem. It may be easier to use a chart or table to solve the problem. Make a table of the pay for each year by adding the raises to the initial pay:

Year 1 Year 2 Year 3

Job 1 Salary $22,000 $26,000 ($22,000 + $4,000) $30,000 ($26,000 + $4,000)

Job 2 Salary $26,000 $28,000 ($26,000 + $2,000) $30,000 ($28,000 + $2,000)

Answer: You will make the same money in the two jobs in the third year.

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KeyTrain Applied Mathematics

Level 6 Problem Solving

Using a Diagram to Solve a Problem Here is another example where a diagram is useful: You are planting a garden in the corner of your backyard. You begin by planting one plant in the corner. Then you plant 3 plants in a diagonal on the second row. Next you plant 5 plants in the third diagonal row. How many plants will you need in the fifth row?

Again, the facts and questions are easy. But setting up the problem is not. This problem become much easier if you make a drawing: 1st row

2nd row

3rd row

4th row

5th row

The fifth row will have 9 plants.

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Page 8

KeyTrain Applied Mathematics

Level 6 Problem Solving

Guessing and Testing In some situations, guessing and testing is a very effective problem-solving method. It is especially useful when the answer must be selected from a fixed number of choices. (For example, if you know the answer is a whole number and not a decimal or fraction.) These are the common steps for solving a problem with guessing and testing: 1) Guess an answer to the problem. 2) Test to see if the answer is correct. 3) If the answer is correct, you are done. If not, then adjust your guess and try again. Note that your second (and third) guesses should be better as you learn from your first guess.

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Page 9

KeyTrain Applied Mathematics

Level 6 Problem Solving

Using Guessing and Testing to Solve a Problem Here is a problem that can be solved with guessing and testing: A manager for Tapes “R” Us has budgeted $220 this week for new merchandise for her store. Video cost $24.95 including tax. Cassettes cost $12.95 including tax. She wants to purchase exactly 10 items. How many videos and how many cassettes should she buy to use the most of her budget? As before, start with the basic steps: What is the problem asking? How many videos and cassettes to buy. What are the facts? Must buy 10 items, and comes as close as possible to $220. Videos cost $24.95, cassettes cost $12.95 Use guess and test: First Guess: 5 Videos 5 x $24.95 = $124.95 5 Cassettes 5 x $12.95 = $ 64.75 TOTAL: $189.70 (Not enough spent, so order more videos since they are more expensive.) Second Guess: 7 Videos 7 x $24.95 = $174.65 3 Cassettes 3 x $12.95 = $ 38.85 TOTAL: $213.50 (Pretty close to $220. If you try 8 videos and 2 cassettes, you will see that it is over $220.) Therefore the answer is 7 videos and 3 cassettes.

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KeyTrain Applied Mathematics

Level 6 Problem Solving

Here is another example of how to guess answers even when you have an equation: You produced two barrels of a chemical. The first barrel weighed twice as much as the second barrel. Together the two barrels weighed 21 pounds. What was the weight of each barrel? As before, start with the basic steps: What is the problem asking? What is the weight of each barrel? What are the facts? The weight of the first barrel, A, is twice the weight of the second barrel, B. Together they weight 21 lbs., so A + B = 21 Use guess and test: First Guess: The second barrel, B weighs 10 lbs. Therefore the first barrel, A, must weigh 2 x 10 = 20 lbs. The total weight would then be 10 + 20 = 30 lbs. (Too heavy – they are only supposed to be 21 lbs. Try a lower number.) Second Guess: The second barrel, B, weighs 8 lbs. Therefore the first barrel, A, must weight 2 x 8 = 16 lbs. The total weight would then be 8 + 16 = 24 lbs. (Still too heavy – they are only supposed to be 21 lbs. Try a lower number.) Third Guess: The second barrel, B, weighs 7 lbs. Therefore the first barrel, A, must weight 2 x 7 = 14 lbs. The total weight would then be 7 + 14 = 21 lbs. Correct! Copyright © 2000, SAI Interactive, Inc. For use only by Chicago Public Schools. Page 11

KeyTrain Applied Mathematics

Level 6 Problem Solving

Working Backwards Sometimes you may know the final result of a problem or math calculation. You may be asked to find the beginning numbers or data. To solve these problems you can work the problem backwards. Simply reverse the order of the math operations. Here is an example of a problem that can be worked backwards: Mr. Lund runs a sporting goods store. He sells a rod and reel in a case for $162. To determine the selling price, he added $10 for the case to the cost of the rod and reel. Then he doubled the total for his markup. Finally, he added a $12 sales tax. How much did the rod and reel cost Mr. Lund? As before, start with the basic steps: What is the problem asking? Find the original cost of the rod and reel (without the case, markup or sales tax). What are the facts? Mr. Lund charged $162, which he found by taking the cost of the rod and reel, adding $10, then multiplying by 2 for markup, then adding $12 for tax. To solve the problem: Perform the math steps in reverse order using the reverse operations (when he added, you subtract and when he multiplied you divide).

Reverse the sales tax : $162 - $12 = $150 Reverse the markup : $150 ÷ 2 = $75 Reverse adding the case : $75 - $10 = $65 He paid $65 for the rod and reel. Check your answer by performing the calculations forward again.

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KeyTrain Applied Mathematics

Level 6 Problem Solving

Solve a Similar but More Simple Problem This strategy works great when you are working with larger numbers, fractions or decimals. These numbers can sometimes make the problem confusing. To decide how to solve the problem, make up a similar problem situation where the numbers are smaller and easier to understand. Then use the same strategy to solve your problem. Here is a problem where fractions and unit conversions make the problem appear more difficult: How many packages will 5 ½ pounds of raisins fill if each package holds 9 ounces?

As before, start with the basic steps: What is the problem asking? Find the number of full packages of raisins you can make. What are the facts? You have 5 ½ pounds of raisins. Each package must have 9 ounces of raisins. Solve the problem: If the numbers are confusing, imagine a more simple problem using different numbers. For instance: How many packages will 10 pounds of raisins fill if each package holds 2 pounds? Here the answer is easy. You could fill 5 packages. You find this by dividing 10 lbs. by 2 lbs. (the total amount of raisins by the amount in each bag).

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KeyTrain Applied Mathematics

Level 6 Problem Solving

Therefore you know that to solve the original problem, you must divide the total amount of raisins (5 ½lbs.) by the amount in each bag (9 ounces). To do this, you must first convert the different weights to the same unit of measurement. 1 How many packages will 5 pounds of raisins fill if each package 2 holds 9 ounces? To solve, convert the pounds to ounces : 1 16 ounces = 88 ounces 5 lbs. = 5.5 lbs. × 2 1 pound Then divide to find the answer : 88 ounces ÷ 9 ounces = 9.7678... The answer is 9 full packages. (There will be some extra raisins, but not enought for another full package.)

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KeyTrain Applied Mathematics

Level 6 Problem Solving

Summary -- Problem Solving Strategies This section has reviewed four strategies for solving more difficult problems: • Using a Drawing or Diagram • Guess and Test • Working Backwards • Solving a More Simple Problem You may want to use these methods in problems later in this level. If you find a problem to be particularly difficult, then see if one of these methods can help you.

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KeyTrain Applied Mathematics

Level 6 Multiple Steps

Level 6 Applied Mathematics Multiple Steps Solving problems in level 6 may require several steps. Often this may involve converting measurement units before performing other calculations. For example, say you need to add two lengths. However one length is given in inches and the other is given in yards. You must then convert the lengths to the same units before adding. If you need unit conversion factors during any of these problems, you can refer to the page of Formulas on the next page.

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KeyTrain Applied Mathematics

Level 6 Multiple Steps

Formulas and Conversions MEASUREMENT Distance 1 foot (ft.) = 12 inches (in.) 1 yard (yd.) = 3 feet 1 mile (mi.) = 5,280 feet

Electricity 1 kilowatt-hour = 1,000 watt-hours amps = watts / volts

1 mile ≈ 1.61 kilometers (km.) 1 inch = 2.540 centimeters (cm.) 1 foot = 0.3048 meters (m.) 1 meter = 1,000 millimeters (mm.) 1 meter = 100 centimeters 1 kilometer = 1,000 meters 1 kilometer ≈ 0.62 miles

FORMULAS

Area 1 square foot (sq. ft.) = 144 square inches (sq. in.) 1 square yard (sq. yd.) = 9 square feet 1 acre = 43,560 square feet

Rectangular Solid (Box) volume = length x width x height

Volume 1 cup (C.) = 8 fluid ounces 1 quart (qt.) = 2 pints (pt.) = 4 cups 1 gallon (gal.) = 4 quarts 1 gallon (gal.) = 231 cubic inches (cu. in.) 1 liter (l.) ≈ 0.264 gallons = 1.056 quarts 1 cubic foot (cu. ft.) = 1,728 cubic inches 1 cubic foot = 7.48 gallons 1 cubic yard (cu. yd.) = 27 cubic feet 1 board foot = 1 inch by 12 inches by 12 inches

(x is used to indicate multiply pi is equal to 3.14) Rectangle perimeter = 2(length + width) area = length x width

Cube volume = (length of side)3 Triangle sum of angles = 180° area = ½ (base x height) Circle number of degrees in a circle = 360° circumference ≈ 3.14 x diameter or pi x diameter area ≈ 3.14 x (radius)2 or pi x (radius)2

Weight 1 ounce (oz.) ≈ 28.350 grams (g.) 1 pound (lb.) = 16 ounces 1 pound ≈ 453.592 grams 1 milligram (mg.) = 0.001 grams 1 kilogram (kg.) = 1,000 grams 1 kilogram ≈ 2.2 pounds 1 ton = 2,000 pounds

Cone volume ≈ 3.14 x (radius)2 x height 3

Temperature °C = .56(°F – 32) or 5/9(°F – 32) ° F = 1.8(°C) + 32 or (9/5 x °C) + 32

Sphere (Ball) volume ≈ 4 x 3.14 x (radius)3 3

Cylinder volume ≈ 3.14 x (radius)2 x height or pi x (radius)2 x height

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KeyTrain Applied Mathematics

Level 6 Multiple Steps

Basic Method for Solving Word Problems Remember that longer or complicated word problems are not really any more difficult than shorter problems. The math operations are the same. Just break the problem down into smaller parts. Solve the smaller parts, and then you can find the answer easily! As before, remember to use the basic method for solving word problems: 1. Read the problem. Find what it is asking. 2. Write down the facts you have. 3. Set up and solve the problem. 4. Check your answer.

Example of a Multiple-step Problem During one winter day the temperature on Sunday was 35°F. During the rest of the week, the temperature dropped 7 degrees each day. What was the temperature on Saturday?

Actually, this is just a subtraction problem. But before subtracting the temperature, you need to know how many days passed from Sunday to Saturday. By counting the days, you can find that 6 days have passed. If this is not clear, you can use a diagram to help: 1 Sunday

2 Monday

3 Tuesday

4 Wednesday

5 Thursday

6 Friday

Saturday

Then you can determine the temperature of Saturday: 35°F - (6 x 7°F) = 35°F - 42°F = -7°F

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KeyTrain Applied Mathematics

Level 6 Multiple Steps

Types of Problems This section will deal with the following types of problems: • Quantities • Positive and Negative Numbers, and • Money. These topics have been covered in general in earlier sections. If you need some review of these topics, go back to the appropriate sections in Levels 3, 4 or 5.

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KeyTrain Applied Mathematics

Level 6 Multiple Steps

Multiple Steps Problem 1 A person earned $100 a week for 15 weeks. He puts $35.75 into a savings account each of these weeks and spends the rest. How much does he spend during the 15 weeks? Check the correct answer. _____ A.

$536.25

_____ B.

$963.75

_____ C.

$1,063.75

_____ D.

$1,500.00

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KeyTrain Applied Mathematics

Level 6 Multiple Steps

Multiple Steps Problem 2 Refer to the table below to answer this question.

Calcium and Sodium in Breakfast Foods FOOD Bacon Butter Coffee Corn Flakes Egg Syrup Milk Orange Juice Pancake Toast Tomato Juice

SERVING 2 pieces 1 pat 250 ml 25 g 1 20 ml 250 ml 250 ml 27 g 1 slice 250 ml

CALCIUM 2 mg 1 mg 0 4 mg 28 mg 25 mg 291 mg 25 mg 27 mg 21 mg 17 mg

SODIUM 325 mg 41 mg 0 251 mg 50 mg 4 mg 120 mg 4 mg 115 mg 170 mg 740 mg

As a dietitian, your patient is on a low-sodium diet (less than 1,100 mg of sodium per meal). She has a breakfast of orange juice, corn flakes, milk, 2 slices of toast with one pat of butter each and coffee. How much sodium did the patient have for breakfast? Check the correct answer. _____ A.

364 mg

_____ B.

586 mg

_____ C.

756 mg

_____ D.

797 mg

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KeyTrain Applied Mathematics

Level 6 Multiple Steps

Multiple Steps Problem 3 Refer to the table below to answer this question.

Calcium and Sodium in Breakfast Foods FOOD Bacon Butter Coffee Corn Flakes Egg Syrup Milk Orange Juice Pancake Toast Tomato Juice

SERVING 2 pieces 1 pat 250 ml 25 g 1 20 ml 250 ml 250 ml 27 g 1 slice 250 ml

CALCIUM 2 mg 1 mg 0 4 mg 28 mg 25 mg 291 mg 25 mg 27 mg 21 mg 17 mg

SODIUM 325 mg 41 mg 0 251 mg 50 mg 4 mg 120 mg 4 mg 115 mg 170 mg 740 mg

As a dietitian, your patient is on a low-sodium diet (less than 1,100 mg of sodium per meal). On another day, your patient has orange juice, 2 slices of bacon, 3 eggs, 2 slices of toast with butter and milk. Is she still following her diet plan of 1,100 mg of sodium per meal? Check the correct answer. _____ A.

Yes

_____ B.

No

_____ C.

Cannot tell

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KeyTrain Applied Mathematics

Level 6 Multiple Steps

H HOSPITAL

Multiple Steps Problem 4 On Monday Memorial Hospital had 100 patients. Tuesday it received 15 new patients and discharged 3. Wednesday it received 9 and discharged 12. Thursday it received 5 and discharged 2, and Friday it received 13 and discharged 5. How many patients were in the hospital at the end of the day Friday? Check the correct answer. _____ A.

36

_____ B.

80

______ C.

120

_____ D.

164

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KeyTrain Applied Mathematics

Level 6 Multiple Steps

Multiple Steps Problem 5 A checking account has $500 to pay installment payments with. The payments were $35 a month for 4 months and then $25 a month for 3 months. How much was left in the account after the payments were made? Check the correct answer. _____ A.

$285

_____ B.

$360

_____ C.

$425

_____ D.

$440

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KeyTrain Applied Mathematics

Level 6 Multiple Steps

Positive and Negative Numbers The next couple of problems involve both positive and negative numbers. As a review, remember these rules for doing math with positive and negative numbers: Adding If the numbers have the same sign, add the numbers and use the same sign:

4 + 9 = 13

(Same as 4 + 9 = 13)

(-5) + (-6) = (-11)

(5 + 6 = 11, but with a negative sign since both were negative.)

If the numbers have different signs, subtract and use the sign of the larger number: (-3) + 5 = 2 9 + (-15) = - 6

(5 - 3 = 2, and 5 is larger than 3, 5 is positive, so the answer is positive) (15 - 9 = 6, and 15 is larger than 9, 15 is negative so the answer is negative)

Subtracting Change the sign of the number being subtracted, then add as shown above: 2 - 5 = 2 + (-5) = -3

-7 - 6 = -7 + (-6) = -13 -3 - (-8) = -3 + 8 = 5 9 - (-4) = 9 + 4 = 13 Multiplying or Dividing If both numbers are the same sign, then the answer is positive. 7 × 3 = 21 42 ÷ 7 = 6

- 8 × - 4 = 32

- 54 ÷ (-6) = 9

If the numbers have different signs, then the answer is negative. - 9 × 6 = - 54 - 56 ÷ 8 = - 7 49 ÷ (-7) = - 7

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KeyTrain Applied Mathematics

Level 6 Multiple Steps

Multiple Steps Problem 6 One day the temperature rose 5 degrees in the morning, then it dropped 9 degrees in the afternoon. The temperature at dawn was 3 degrees below. What was the temperature at the end of the day? Check the correct answer. _____ A.

-7 degrees

_____ B.

-1 degree

_____ C.

1 degree

_____ D.

7 degrees

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KeyTrain Applied Mathematics

Level 6 Multiple Steps

Multiple Steps Problem 7 The highest and lowest temperatures recorded in New York one year were 38 degrees Celsius and –21 degrees Celsius. The next year the highest and lowest temperatures were 36°C and -25°C. What was the difference in the lowest and highest temperatures over the two years? Check the correct answer. _____ A.

13°C

_____ B.

17°C

_____ C.

61°C

_____ D.

63°C

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KeyTrain Applied Mathematics

Level 6 Multiple Steps

Multiple Steps Problem 8 When you last balanced your checkbook, you had $463.76. You then wrote checks for $12.56, $52.11 and $26.03. You deposited $101.32 and $10.98. Your bank says your balance is $485.36, but your checkbook says $511.39. What, if anything, did you do wrong in tracking your checking account? Check the correct answer. _____ A.

Nothing, the bank is wrong.

_____ B.

Carried wrong when adding $52.11.

_____ C.

Forgot to subtract $26.03 check.

_____ D.

Forgot to add $10.98 deposit.

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KeyTrain Applied Mathematics

Level 6 Multiple Steps

Summary – Multiple Step Problems The problems in this section were not highly complex. They just required more than one calculation or comparison. The key to solving longer problems is to see them as a series of smaller, easier problems. If you can see this in the problems you face, you will be able to solve much more difficult problems than these were. You will see problems like this in the next sections.

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KeyTrain Applied Mathematics

Level 6 Fractions and Decimals

Level 6 Applied Mathematics Fractions and Decimals This section has problems dealing with fractions and decimals. These problems use the same mathematical operations that were covered in the Level 5 section on fractions and decimals. These include: addition, subtraction, multiplication and division. The difference here is that there may be several steps required to solve the problem. Again, break the problem down into smaller steps. By solving each smaller, easy step, the larger problem can be solved.

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KeyTrain Applied Mathematics

Level 6 Fractions and Decimals

Review Basic Math Operations with Fractions Adding and Subtracting Fractions

If the fractions have the same denominator, just add or subtract the numerators with the same denominator:

1 2 1 1 + = = 4 4 4 2

5 2 3 = 4 4 4

2 1 3 + = =1 3 3 3

3 4 1 - = 5 5 5

If the denominators are different, you must convert one or both fractions to the same denominator. Then add or subtract the numerator: 5 2 3 1 1 + = + = 6 6 6 3 2

1 9 5 3 10 = = 6 4 12 12 12

Multiplying Fractions

To multiply fractions, simply multiply the numerators together, and multiply the denominators together: 2 3 6 1 × = = 3 4 12 2 Dividing Fractions

To divide fractions, invert the dividing fraction and then multiply: 1 2 11 11 121 1 2 ×3 = × = = 8 5 3 15 15 5 3 Mixed Numbers Convert the mixed numbers to fractions and then proceed as above: 3 8 4 2 1 4 ÷ = × = =1 5 5 5 1 2 5

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KeyTrain Applied Mathematics

Level 6 Fractions and Decimals

Fractions and Decimals Problem 1 3 1 A bar of steel that measures 16 feet long weighs 105 pounds. 4 2 How much does a one-foot section of steel weight? (use decimals) Check the correct answer.

_____ A.

3.2 lbs.

_____ B.

6.4 lbs.

_____ C.

6.6 lbs.

_____ D.

7.2 lbs.

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KeyTrain Applied Mathematics

Level 6 Fractions and Decimals

Fractions and Decimals Problem 2 Drill bits are made from drill rod. Each bit is 4 You must allow

1 inches long. 16

5 inch waste for each drill made. 32

How many inches of rod are needed to make 15 drills? Check the correct answer. 7 32

_____ A.

4

_____ B.

60

_____ C.

63

9 32

_____ D.

69

3 32

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KeyTrain Applied Mathematics

Level 6 Fractions and Decimals

Fractions and Decimals Problem 3 You must drill 5 equally spaced holes in a line along a board. The holes will measure 4 3/8 inches apart, center to center. The holes are 3/4" in diameter. What is the total length of the holes (i.e. the distance between the end holes, including the holes)? Check the correct answer. _____ A.

1 17 inches 2

_____ B.

7 17 inches 8

_____ C.

1 18 inches 4

_____ D.

1 20 inches 2

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KeyTrain Applied Mathematics

Level 6 Fractions and Decimals

Fractions and Decimals Problem 4 A customer wants to carpet a family room measuring 14' 6" by 22' 9" and a hallway that is 4' by 9'8". Ignoring any waste, about how much carpet is needed for this job? Check the correct answer. _____ A.

37 sq. yd.

_____ B.

41 sq. yd.

_____ C.

330 sq. yd.

_____ D.

396 sq. yd.

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KeyTrain Applied Mathematics

Level 6 Fractions and Decimals

Fractions and Decimals Problem 5 Three electrical appliances have power ratings of 1 7/8 watts, and 2 other appliances have power ratings of 4 3/4 watts. What is the total power used by these appliances? Check the correct answer.

_____ A.

5 5 watts 8

_____ B.

5 6 watts 8

_____ C.

1 10 watts 4

_____ D.

1 15 watts 8

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KeyTrain Applied Mathematics

Level 6 Fractions and Decimals

Fractions and Decimals Problem 6 A jeweler is making a copy of a 15-inch chain to sell in his store. The clasp is 1/2 inch long. Each link in the chain is 1/4 inch long. How many links must be used to make the chain? Check the correct answer. _____ A.

4

_____ B.

30

_____ C.

58

_____ D.

60

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KeyTrain Applied Mathematics

Level 6 Fractions and Decimals

Fractions and Decimals Problem 7 Your co-worker packed a case of 12 gears for shipment. Each gear weighs 1 lb. 3 oz. The box and packing weigh 2 lbs. He marked the shipping weight of the box as 15.6 lbs. Is the shipping weight correct? If not, why? _____ A.

Yes, it is correct.

_____ B.

No, he forgot to add the box weight.

_____ C.

No, he converted the ounces wrong.

_____ D.

No, he only counted 10 gears.

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KeyTrain Applied Mathematics

Level 6 Fractions and Decimals

Summary – Fractions and Decimals These problems have used fractions in more complicated calculations. These may include finding common denominators, converting mixed numbers, or several math operations. Simply focus on what math operations are required to solve the problem. Then you can convert denominators or mixed numbers as you need to solve the equations.

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KeyTrain Applied Mathematics

Level 6 Percentages

Level 6 Applied Mathematics Percentages In Level 5, you saw how percentages can be used to describe portions of a larger amount. Level 5 problems usually asked to find a portion, or percentage, of a larger number. An example of this is finding the sale price of a $10 shirt that is on sale for 30% off. The answer would be $7. ($10 - 30% of $10.) In Level 6, some of the problems may work the opposite way. The problem may give an amount that is a certain percentage of a larger number. The answer will be to find the larger amount. An example of this would be finding the regular price of a shirt that has been marked down by 30% and is now on sale for $7. The answer is $10.

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KeyTrain Applied Mathematics

Level 6 Percentages

Percentages As a review, percent means the number of parts out of 100 total parts: 100% =

100 100

= 1.0

100% of the circle is green.

50% =

50 100

=

1 2

= 0.5

25% =

50% of the circle is green.

25 100

=

1 4

= 0.25

25% of the circle is green.

Finding the Percentage of a Number As a review, you can find the percentage of a number using a ratio, or by multiplying by the percentage as a fraction or decimal. For example, what is 75% of 80? Using a ratio: You know that 75% mans 75 parts of 100. Set up equal fractions to find how many parts out of 80 is equal to 75 parts of 100. Then cross multiply.

75 100

=

X 80

100 × X = 75 × 80

X = 75 × 80 ÷ 100 = 60

By multiplying by the percentage as a fraction or decimal: Convert the percentage to a decimal and multiply. 75 75% = = 0.75 0.75 × 80 = 60 100

As you become familiar with fractions, you will probably find the second method to be faster. You will know that 75% is the same as multiplying by 0.75. Copyright © 2000, SAI Interactive, Inc. For use only by Chicago Public Schools. Page 41

KeyTrain Applied Mathematics

Level 6 Percentages

Find the Percentage One Number is of Another

Some problems may give two numbers, and ask how many percent one is of another. For instance, how many percent is 8 of 24? Here is how this might be asked: Most businesses have an eight-hour workday. What percent of the day are most workers at their jobs?

You can use a proportion or ratio to solve this problem. (You know a day has 24 hours.)

8 X = 24 100 Cross multiply : X × 24 = 8 × 100

X = 8 × 100 ÷ 24 = 33%

8 Method 2 : Find the equivalent decimal by dividing then convert to percent : 24 8 ÷ 24 = 0.333 0.333 ⎯ ⎯→ 33%

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Level 6 Percentages

Percentages Problem 1 Find the percentage described to the nearest whole number.

163 is what percent of 921.5? Answer:

Percentages Problem 2 Find the percentage described to the nearest whole number.

516.5 is what percent of 675.7? Answer:

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Level 6 Percentages

Percentages Problem 3 Find the percentage described to the nearest whole number.

325.7 is what percent of 678.3? Answer:

Percentages Problem 4 Find the percentage described to the nearest whole number.

157.8 is what percent of 273? Answer:

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Level 6 Percentages

Percentages Problem 5 Find the percentage described to the nearest whole number. 269.2 is what percent of 744.9? Answer:

Percentages Problem 6 Find the percentage described to the nearest whole number. 24.3 is what percent of 695.7? Answer:

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Level 6 Percentages

Percentages Problem 7 Find the percentage described to the nearest whole number.

300.2 is what percent of 656.4? Answer:

Percentages Problem 8 Find the percentage described to the nearest whole number.

35.4 is what percent of 61.4? Answer:

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Level 6 Percentages

Percentages Problem 9 Find the percentage described to the nearest whole number.

582.1 is what percent of 990.2? Answer:

Percentages Problem 10 Find the percentage described to the nearest whole number.

301.5 is what percent of 593.2? Answer:

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KeyTrain Applied Mathematics

Level 6 Percentages

Finding a Number when a Percent of it is Known In Level 6 problems may ask to find a number by giving a known percentage of that number. For instance: In a recent survey, 160 teenagers said that television influences them to buy advertised products. The survey summary states that 80% of teenagers said that TV influences their buying. How many teenagers were surveyed?

From this statement, you know that 160 teenagers must have been the 80% of all the teenagers that were surveyed. So you must determine what number 160 is 80% of. In other words, what number times 80% gives 160? X × 80% = X × 0.80 = 160; You could also use a ratio :

160 X

Cross multiply :

=

so X = 160 ÷ 0.80 = 200

80 100

X × 80 = 160 × 100;

X = 160 × 100 ÷ 80 = 200

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Level 6 Percentages

Percentages Problem 11 Find the number described to the nearest whole number.

124.44 is 34 percent of what number? Answer:

Percentages Problem 12 Find the number described to the nearest whole number.

11.32 is 4 percent of what number? Answer:

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Level 6 Percentages

Percentages Problem 13 Find the number described to the nearest whole number.

291.3 is 30 percent of what number? Answer:

Percentages Problem 14 Find the number described to the nearest whole number.

73.26 is 33 percent of what number? Answer:

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Level 6 Percentages

Percentages Problem 15 Find the number described to the nearest whole number.

18 is 25 percent of what number? Answer:

Percentages Problem 16 Find the number described to the nearest whole number.

70.3 is 37 percent of what number? Answer:

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KeyTrain Applied Mathematics

Level 6 Percentages

Percentages Problem 17 Find the number described to the nearest whole number.

9.12 is 24 percent of what number? Answer:

Percentages Problem 18 Find the number described to the nearest whole number.

2.21 is 17 percent of what number? Answer:

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KeyTrain Applied Mathematics

Level 6 Percentages

Percentages Problem 19 Find the number described to the nearest whole number.

398.61 is 43 percent of what number? Answer:

Percentages Problem 20 Find the number described to the nearest whole number.

443.3 is 62 percent of what number? Answer:

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KeyTrain Applied Mathematics

Level 6 Percentages

Percentages Word Problems Here is an example of a word problem that finds a number knowing a percentage of that number: Five percent of a batch of fuses was found to be defective. If 32 fuses were defective, how many fuses were inspected?

1.

First, read the problem carefully. What is the problem asking? How many fuses were inspected?

2.

What are the facts? 5% of the fuses were defective. 32 were found to be defective.

3.

Set up and solve the problem. 5% of what number equals 32? 0.05 × X = 32 X = 32 ÷ 0.05 = 640

4.

Check that the answer is reasonable. Check by finding the number defective 640 × 5% = 640 × 0.05 = 32 Using a calculator, this checks ok.

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Level 6 Percentages

Percentages Problem 21 Twenty-five percent (25%) of the homes in a neighborhood have computers. If 50 homes in the neighborhood have computers, how many homes are there? _____ A.

12.5

_____ B.

75

_____ C.

100

_____ D.

200

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KeyTrain Applied Mathematics

Level 6 Percentages

Finding the Percent Increase or Decrease Changes are often described in terms of a percentage increase or decrease. The percentage change is always the percentage that the change is of the original amount. Percentage change =

Amount of change Original amount

× 100%

Consider a salary increase from $72 per day to $90 per day. What is the percent increase?

Amount of change = 90 - 72 = 18 Percent increase =

18 72

× 100% = 0.25 × 100% = 25%

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Level 6 Percentages

Percentages Problem 22 Find the percent described to the nearest whole number.

What is the percent increase from 614 to 1,031.52? Answer:

Percentages Problem 23 Find the percent described to the nearest whole number.

What is the percent increase from 345 to 451.95? Answer:

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Level 6 Percentages

Percentages Problem 24 Find the percent described to the nearest whole number.

What is the percent increase from 508 to 706.12? Answer:

Percentages Problem 25 Find the percent described to the nearest whole number.

What is the percent increase from 843 to 1,382.52? Answer:

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Level 6 Percentages

Percentages Problem 26 Find the percent described to the nearest whole number.

What is the percent increase from 839 to 1,627.66? Answer:

Percentages Problem 27 Find the percent described to the nearest whole number.

What is the percent decrease from 255 to 140.25? Answer:

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Level 6 Percentages

Percentages Problem 28 Find the percent described to the nearest whole number.

What is the percent decrease from 592 to 444? Answer:

Percentages Problem 29 Find the percent described to the nearest whole number.

What is the percent increase from 852 to 1,618.8? Answer:

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Level 6 Percentages

Percentages Problem 30 Find the percent described to the nearest whole number.

What is the percent increase from 11 to 11.44? Answer:

Percentages Problem 31 Find the percent described to the nearest whole number.

What is the percent decrease from 423 to 16.92? Answer:

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Level 6 Percentages

Discounts Discounts is just another word for saying a percent decrease. Green Thumb Nursery ordered $175 worth of seeds. When they ordered, they got a 15% discount because the order was over $100. How much did they pay for the seeds?

The 15% discount means the price was reduced by 15%. Remember that : Amount of change × 100% Percentage change = Original amount The percent change is 15%, and the original amount is $175. So 15% =

change $175

× 100%

The change is then $175 × 15% = $175 × 0.15 = $26.25 So they actually paid the original - the change = $175 - $26.25 = $148.75

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Level 6 Percentages

Percentages Problem 32 One day in March, 75% of the stores' customers paid with credit cards. If there were 50 customers that day, how many used a credit card? Check the correct answer. _____ A.

13

_____ B.

25

_____ C.

38

_____ D.

40

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Level 6 Percentages

Percentages Problem 33 Shares of stock were sold and a profit of $1,320 was made. The profit was 15% over a 30-day period. How much were the shares worth when they were originally purchased? Check the correct answer. _____ A.

$198

_____ B.

$1,122

_____ C.

$8,000

_____ D.

$8,800

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KeyTrain Applied Mathematics

Level 6 Percentages

Percentages Problem 34 Recently at a theater, they were evaluating attendance at several events. From the first event to the second event the attendance dropped from 250 to 230. Find the percent decrease to the nearest percent? Check the correct answer. _____ A.

8%

_____ B.

9%

_____ C.

20%

_____ D.

92%

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Level 6 Percentages

Percentages Problem 35 You have determined that you saved $12.50 when you bought a pair of jeans on sale. They were on sale for 25% off. What was the original price and what was the sale price? Check the correct answer. _____ A.

$25.00, $12.50

_____ B.

$50.00, $12.50

_____ C.

$37.50, $50.00

_____ D.

$50.00, $37.50

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Level 6 Percentages

Percentages Problem 36 A hardware store owner bought a used refrigerator for $155 and marked it to sell for a profit of 30% on the cost. He then sold it for 10% less than the marked price. What was the selling price? Check the correct answer. _____ A.

$170.50

_____ B.

$181.35

_____ C.

$186.00

_____ D.

$201.50

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KeyTrain Applied Mathematics

Level 6 Percentages

Percentages Problem 37 Using the same refrigerator sale: A hardware store owner bought a used refrigerator for $155 and marked it to sell for a profit of 30% on the cost. He then sold it for 10% less than the marked price. What is the percent profit made by the owner? Check the correct answer. _____ A.

15%

_____ B.

17%

_____ C.

19%

_____ D.

30%

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Level 6 Percentages

Percentages Problem 38 A sales person receives $250 per week and a 3% commission on all sales over $5,000. What are her total earnings if her weekly sales totaled $9,525? Check the correct answer. _____ A.

$135.75

_____ B.

$285.75

_____ C.

$385.75

_____ D.

$535.75

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Level 6 Percentages

Percentages Problem 39 A dealer sells air compressors at 20% off of the manufacturer's suggested retail price (MSRP). Then the dealer had a sale where she took an additional 30% off of hes normal price. If the MSRP was $180 and the dealer charged $90, did she charge you right? If not, why? Is the price correct? If not, why? Check the correct answer. _____ A.

Yes, it is correct.

_____ B.

No, she took only the 30% off MSRP

_____ C.

No, she forgot to take the 30% off.

_____ D.

No, she took 30% off of the MSRP, not the normal price.

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Level 6 Percentages

Percentages Summary This section has included several different types of problems using percentages. These included finding the percentage increase or decrease, determining the total from a percentage of the total, and finding discounts and markups. As you can see, there are many different words and terms used to describe percentages. The key to working with more complicated problems is to read them carefully. You can always use the same ratio to solve the problem. However you need to be careful to put the right numbers in the right place! This is another place where practice can save you money. When you are buying items on sale, make sure you are getting the full discount that was advertised!

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Level 6 Area and Volume

Level 6 Applied Mathematics Area and Volume Many jobs require calculations of area and volume. Construction, engineering, landscaping, decorating, surveying and sewing are all examples where this type of math is essential to making the most of your resources. In Level 6, problems will involve manipulating the area of squares, rectangles, circles and triangles. Other problems will deal with the volume of rectangular solids.

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Level 6 Area and Volume

Perimeter, Area and Volume As a review, recall the difference between perimeter, area and volume:

8 ft.

6 ft.

6 ft.

8 ft. Perimeter The total length around the outside of an object. Perimeter = 6 ft. + 8 ft. + 6 ft. + 8 ft. = 28 ft. Area The surface area of a flat shape. Area = 6 ft. x 8 ft. = 24 sq. ft. Volume The total size of a 3-dimensional object. This is like the amount an object could hold if it were a container.

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Level 6 Area and Volume

Area of a Rectangle As was mentioned in Level 5, the area of a region is the number of square units of space needed to cover the region. For instance, the size of rooms in a house can be measured in square feet. The area of a rectangle or square can be found by multiplying the length by the width: Area = Length x Width Suppose you wanted to cover the area shown below with one-foot square tiles. To determine the number of tiles, you would multiply 7 x 8 = 56 tiles. This is the same as finding the area in square feet. 8 ft.

7 ft.

Length x Width = Area 8 ft. x 7 ft. = 56 sq. ft.

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Level 6 Area and Volume

Rearranging a Formula for Area Sometimes the formula needs to be altered or reversed to solve a problem. If the area and width of a rectangle are given, then rearrange the formula to find the length. 22 in. ? in.

352 sq. in.

Example: If the area of a rectangle is 352 square inches, and the length is 22 inches, what is its width?

Area = Length x Width Rearrange the equation to find the width: (Remember that division is the opposite of multiplication.)

Width = Area ÷ Length Width = 352 sq. in. ÷ 22 in. = 16 in.

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Level 6 Area and Volume

Using Area to Solve a Word Problem Here is an example of using area to solve a word problem: You are laying out a new retail store and need to arrange some displays. You know that the store is 8,800 sq. ft. in size, and that it is 110 ft. wide. How deep (from front to back) is the store?

1. First, read the problem carefully. What is the problem asking? What is the length (depth) of the store? 2. What are the facts? The store is 8,800 sq. ft. in area and 110 ft. wide. 3. Set up and solve the problem. Area = Length × Width Length = Area ÷ Width Length = 8,800 ÷ 110 = 80 ft. 4. Check that the answer is reasonable. Area = 80 ft. x 110 ft. = 8,800 sq. ft.

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Level 6 Area and Volume

Area of a Triangle For a triangle, the area is always one half of the base times the height. For a triangle, Area =

1 × base × height 2

1 × 7 ft. × 8ft. = 28 sq. ft. 2

height - 8 ft.

base – 7 ft.

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Level 6 Area and Volume

Circumference of Circles The perimeter of a circle is called the circumference. The circumference (C) is equal to 3.14 times the diameter. This is normally written as: C = π x d Where π is pi (said like “pie”), and is equal to 3.14159…

radius

diameter

Recall that the diameter (d) is the total width of the circle. The radius (r) is the distance from the center to a point on the circle. The circumference can also be written as: C =π × d = 2×π × r

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Level 6 Area and Volume

Area of Circles The area of a circle (A) is equal to 3.14 times the radius times the radius. This is normally written as: A = π × r × r = π r2 where π is pi (said like " pie"), and is equal to 3.14159...

radius

diameter

Since the radius is equal to half the diameter, A = π × r 2 = π × (d ÷ 2) 2 = π × d 2 ÷ 4

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Level 6 Area and Volume

Area and Volume Problem 1 Please answer the question below. Round the answer to two decimal places. Use π = 3.14 when needed. What is the area of a square that is 7.1 yards on a side? Answer:

Area and Volume Problem 2 Please answer the question below. Round the answer to two decimal places. Use π = 3.14 when needed. What is the perimeter of a square that is 16.8 ft. on a side? Answer:

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Level 6 Area and Volume

Area and Volume Problem 3 Please answer the question below. Round the answer to two decimal places. Use π = 3.14 when needed. What is the area of a square that is 19.8 meters on a side? Answer:

Area and Volume Problem 4 Please calculate the area as described below. Please answer the question below. . Use π = 3.14 when needed. What is the area of a circle that is 12.6 inches in diameter? Answer:

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Level 6 Area and Volume

Area and Volume Problem 5 Please answer the question below. Round the answer to two decimal places. Use π = 3.14 when needed. What is the area of a circle that is 2.2 feet in diameter? Answer:

Area and Volume Problem 6 Please answer the question below. Round the answer to two decimal places. Use π = 3.14 when needed. What is the perimeter (circumference) of a circle that has a radius of 19.3 yards? Answer:

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Level 6 Area and Volume

Area and Volume Problem 7 Please answer the question below. Round the answer to two decimal places. Use π = 3.14 when needed. What is the perimeter (circumference) of a circle that has a radius of 6.5 feet? Answer:

Area and Volume Problem 8 Please answer the question below. Round the answer to two decimal places. Use π = 3.14 when needed. What is the perimeter of a rectangle that is 19.1 inches on one side and 4 inches on the other? Answer:

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Level 6 Area and Volume

Area and Volume Problem 9 Please answer the question below. Round the answer to two decimal places. Use π = 3.14 when needed. What is the area of a rectangle that is 3.4 inches on one side and 4 inches on the other? Answer:

Area and Volume Problem 10 Please answer the question below. Round the answer to two decimal places. Use π = 3.14 when needed. What is the perimeter of a rectangle that is 5.5 ft. by 9.8 ft.? Answer:

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Level 6 Area and Volume

Volume The volume of a container tells the size of the inside of the container. Common measures of volume are the gallon, cup, and cubic foot. To determine the volume of a rectangular solid, multiply the width times the depth times the height:

height = 3 depth = 3 width = 4

Volume = 4 x 3 x 3 = 36

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Level 6 Area and Volume

Figuring Volume Here is a word problem that involves volume:

A shipping container has the following dimensions: length – 7 m., width – 5 m., height – 3 m. You must ship square boxes 1 meter long on each side inside the shipping container. How many boxes will it hold?

1. First, read the problem carefully. What is the problem asking? How many 1 cubic meter boxes will it hold? In other words, what is the volume of the container in cubic meters? 2. What are the facts? The container is 7 meters long by 5 meters wide by 3 meters high 3. Set up and solve the problem: Volume = length × width × height = 7m × 5m × 3m = 105 cubic meters Since the container has dimensions of whole meters, it will hold 105 boxes. 4. Check that the answer is reasonable. One layer of the container holds: 7 x 5 = 35 boxes Three layers high holds: 35 x 3 = 105 boxes.

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Level 6 Area and Volume

Area and Volume Problem 11 You bought a toolbox that is 1 ft. long, 6 inches wide and 8 inches high. What is the volume of this toolbox? _____ A.

48 cubic inches

_____ B.

128 cubic inches

_____ C.

480 cubic inches

_____ D.

576 cubic inches

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Level 6 Area and Volume

Area and Volume Problem 12 A parcel of land has an area of 2 square miles and a width of 6,500 feet. How long is the land? Check the best answer. _____ A.

1.23 miles

_____ B.

8,580 feet

_____ C.

12,989 feet

_____ D.

10,560 feet

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Level 6 Area and Volume

Area and Volume Problem 13 You are carpeting a room 16 feet by 14 feet 6 inches with a rug that costs $18.50 per square foot of finished space. How much would the flooring cost? Check the correct answer. _____ A.

$232

_____ B.

$4,144

_____ C.

$4,292

_____ D.

$4,322

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Level 6 Area and Volume

Area and Volume Problem 14 You have a space in front of your house, 10 feet long and 3 feet wide. You need to put a concrete sidewalk 6 inches thick in this space. How many cubic feet of concrete are needed for this sidewalk? Check the correct answer. _____ A.

12.5 cubic feet

_____ B.

15 cubic feet

_____ C.

30 cubic feet

_____ D.

180 cubic feet

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Level 6 Area and Volume

Area and Volume Problem 15 A 9 foot by 12 foot long rug is placed in a room that has an area of 238 square feet with a length of 17 feet. How much of the room is left uncovered? Check the correct answer. _____ A.

14 square feet

_____ B.

108 square feet

_____ C.

130 square feet

_____ D.

217 square feet

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Level 6 Area and Volume

Area and Volume Problem 16 In square feet, how large a tablecloth will be needed to cover a table that measures 41 inches long and 25 inches wide? How large must the tablecloth be? Check the correct answer. _____ A.

7.1 square feet

_____ B.

10.25 square feet

_____ C.

14.76 square feet

_____ D.

1025 square feet

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Level 6 Area and Volume

Area and Volume Problem 17 A large aquarium is 4 m. long, 2 m. wide and 3 m. deep? How many cubic meters of water will it hold? Check the correct answer. _____ A.

9 cubic meters

_____ B.

24 cubic meters

_____ C.

36 cubic meters

_____ D.

48 cubic meters

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Level 6 Area and Volume

Area and Volume Problem 18 In a new home, the front entry and living room are going to be partially carpeted. The entry measures 10 feet by 9 feet and the living room measures 24 feet by 18 feet. If they carpet 90% of the area, how many square feet of carpet will they need to purchase? Check the correct answer. _____ A.

342 square feet

_____ B.

432 square feet

_____ C.

470 square feet

_____ D.

522 square feet

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Level 6 Area and Volume

Area and Volume Problem 19 One pound of grass seed covers 135 square feet of lawn and costs $4.65. What is the cost of seeding a lawn that measures 15 yards by 12 yards? Check the correct answer. _____ A.

$6.20

_____ B.

$55.80

_____ C.

$120.00

_____ D.

$7,533.00

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Level 6 Area and Volume

Area and Volume Problem 20 A chemical storage bin measures 6 meters by 3 meters by 5.4 meters. How many bins will be needed to store 120 cubic meters of chemical? Check the correct answer. _____ A.

1

_____ B.

2

_____ C.

32

_____ D.

97

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Level 6 Area and Volume

Area and Volume Problem 21 You want to add a cellar to your store. The construction company told you it would cost $5.90 per cubic yard to dig the cellar, plus $20 per square foot to finish it. How much will it cost to add a cellar 36 feet long, 14 feet wide and 8 feet deep? Check the best answer. _____ A.

$881.07

_____ B.

$10,080.00

_____ C.

$10,960.87

_____ D.

$23,788.80

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Level 6 Area and Volume

Area and Volume Problem 22 How many cubic yards of concrete are needed for a driveway that measures 12 feet wide, 81 feet long and 6 inches deep? How many cubic feet of concrete are needed for this driveway? Check the correct answer. _____ A.

97 cubic feet

_____ B.

486 cubic feet

_____ C.

972 cubic feet

_____ D.

5,832 cubic feet

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Level 6 Area and Volume

Area and Volume Problem 23 You are carving a block of ice for a banquet. It measures 1½ feet long, 1½ feet wide and 1½ feet thick? Ice weighs 57 pounds per cubic foot. What is the weight of the ice block? Check the correct answer. _____ A.

3.375 pounds

_____ B.

16.89 pounds

_____ C.

57 pounds

_____ D.

192.375 pounds

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Level 6 Area and Volume

Area and Volume Problem 24 Which has the greater volume: a 6 cm. cube or a rectangle solid with a 3 cm. square base and a height of 12 cm.? Which one is larger? Check the correct answer. _____ A.

The cube

_____ B.

The rectangle

_____ C.

They are the same

_____ D.

There is not enough information

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Level 6 Area and Volume

Area and Volume Problem 25 A moving crate measures 5’3” wide by 3’6” high by 4’9” long. The box is marked 87.3 cubic feet. Is the size marked correct? If not, why? Check the correct answer. _____ A.

Yes, it is correct.

_____ B.

No, forgot to multiply by the height

_____ C.

No, they added instead of multiplying

_____ D.

No, converted in. to ft. wrong.

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KeyTrain Applied Mathematics

Level 6 Area and Volume

Summary – Area and Volume These problems have shown how area and volume can be used to plan many different types of jobs. By calculating ahead, you can save money on materials and estimate the total cost of the job. Be aware that sometimes people do not say the units correctly on area and volume measurements. For instance, carpet is normally sold by the square yard. However the salesperson may simply say "$10 per yard". Similarly, dirt is usually sold by the cubic yard, even though people may say "per yard" for short.

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KeyTrain Applied Mathematics

Level 6 Rate Problems

Level 6 Applied Mathematics Rate Problems A rate is a comparison of two quantities with different units. This is commonly used to describe how fast or how often something occurs. Say you drive 200 miles in 4 hours. What is the rate of travel? In other words, what is your speed?

200 miles = 50 miles per hours 4 hours Rates can be expressed as fractions. The word "in" is like dividing. Therefore the 200 rate of 200 miles in 4 hours is equal to the fraction . The rate is usually spoken 4 with the work " per", as in miles per hour .

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KeyTrain Applied Mathematics

Level 6 Rate Problems

Rates Problem 1 The next 10 problems will give you practice with rates. Please calculate the rate as described below. Round the answer to two decimal places.

68.9 cases in 45 hours equals how many cases per hour?

Answer:

Rates Problem 2 This problem will give you practice with rates. Please calculate the rate as described below. Round the answer to two decimal places.

14 inches in 20 seconds equals how many inches per second?

Answer:

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KeyTrain Applied Mathematics

Level 6 Rate Problems

Rates Problem 3 This problem will give you practice with rates. Please calculate the rate as described below. Round the answer to two decimal places.

8.5 yards in 22 minutes equals how many yards per minute?

Answer:

Rates Problem 4 This problem will give you practice with rates. Please calculate the rate as described below. Round the answer to two decimal places.

92.5 meters in 54 seconds equals how many meters per second?

Answer:

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KeyTrain Applied Mathematics

Level 6 Rate Problems

Rates Problem 5 This problem will give you practice with rates. Please calculate the rate as described below. Round the answer to two decimal places.

66.2 sections in 49 meters equals how many sections per meter?

Answer:

Rates Problem 6 This problem will give you practice with rates. Please calculate the rate as described below. Round the answer to two decimal places.

69.2 parts in 63 shifts equals how many parts per shift?

Answer:

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KeyTrain Applied Mathematics

Level 6 Rate Problems

Rates Problem 7 This problem will give you practice with rates. Please calculate the rate as described below. Round the answer to two decimal places.

86.9 miles in 48 hours equals how many miles per hour?

Answer:

Rates Problem 8 This problem will give you practice with rates. Please calculate the rate as described below. Round the answer to two decimal places.

68.8 dollars in 45 tons equals how many dollars per ton?

Answer:

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KeyTrain Applied Mathematics

Level 6 Rate Problems

Rates Problem 9 This problem will give you practice with rates. Please calculate the rate as described below. Round the answer to two decimal places.

5.5 kilometers in 90 hours equals how many kilometers per hour?

Answer:

Rates Problem 10 This problem will give you practice with rates. Please calculate the rate as described below. Round the answer to two decimal places.

96.3 dollars in 63 hours equals how many dollars per hour?

Answer:

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KeyTrain Applied Mathematics

Level 6 Rate Problems

Predictions and Comparisons In industry, rates are used to make predictions and comparisons. One common example is calculating time rates. If a filter can process 10 gallons of water per minute, then how many gallons of water can it process in one day? To find this, multiply the rate by the number of minutes in a day:

10

gallons minutes hours gallons × 60 × 24 = 14,400 minute hour day day

When you do this, you can see that the same units of measurement on the top and bottom cancel each other out. The minutes in gallons per minute and in minutes per hour cancel, and the same with the hours. Therefore the final rate has the units of gallons per day.

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KeyTrain Applied Mathematics

Level 6 Rate Problems

Multi-Rates Many problems in the workplace involve more than one rate. In Level 6, problems may use several rates or other calculations at once. An example of a multi-rate problem would be:

It takes 11 pipe elbows to assemble one chlorine pump. Your team can assemble four pumps in one day. If you need to order parts for next week (5 working days), how many pipe elbows should you order?

You can calculate this using the rates given:

11

elbows days pumps elbows × 4 ×5 = 220 week week day pumps

You will need to order 220 elbows.

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KeyTrain Applied Mathematics

Level 6 Rate Problems

Rates and Word Problems Here is an example of using rates to solve a word problem:

An employee in a shoe repair store must schedule his day so that he can complete all of his work. To do that, he must know how long it takes to complete each job. One day he worked on 15 shoes from 11:45 a.m. until 4:30 p.m., taking a half hour for lunch. Approximately how long did it take to complete each shoe? 1) First, read the problem carefully. What is the problem asking? How long does it take for each shoe? 2) What are the facts? Worked from 11:45 a.m. to 4:30 p.m. Took half hour for lunch Completed 15 shoes 3) Set up and solve the problem. 1. Find how long he worked: 11:45 to 12:00 is 15 min.; 12:00 to 4:30 is 4 hrs. 30 min.; subtract 30 minutes for lunch Total = 15 min. + (4 hrs. 30 min.) - 30 min. = 15 + (4 x 60 + 30 min.) - 30 min. = 255 minutes

2. Find the rate:

255min. = 17 minutes per shoe 15 shoes 4) Check that the answer is reasonable. 17 minutes x 15 shoes = 255 min. = 4 hrs. 15 min.

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KeyTrain Applied Mathematics

Level 6 Rate Problems

Rates Problem 11 A secretary can type 79 words per minutes. If she works 5 eight-hour days each week, how many words does she type in a week? Check the correct answer. _____ A.

30 words

_____ B.

3,160 words

_____ C.

189,600 words

_____ D.

198,600 words

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KeyTrain Applied Mathematics

Level 6 Rate Problems

Rates Problem 12 Two pumps are used to empty a sewage tank. One pump pumps 60 gallons per minute (60 gpm) and the second pumps 50 gpm. They pumped for 30 minutes. How many total gallons are pumped? Check the correct answer. _____ A.

330

_____ B.

2,500

_____ C.

3,000

_____ D.

3,300

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KeyTrain Applied Mathematics

Level 6 Rate Problems

Rates Problem 13 It takes 2.5 yards of material to make a dress. Harley’s Clothing Design estimates that they can produce 52 dresses each week. How much material will they need to purchase to make dresses for a year? Check the correct answer. _____ A.

130 yards

_____ B.

910 yards

_____ C.

2,704 yards

_____ D.

6,760 yards

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KeyTrain Applied Mathematics

Level 6 Rate Problems

Rates Problem 14 One pump pumps 125 gpm into a mixing tank while another pumps 100 gpm out of the tank. The tank starts with 1,000 gallons. How many gallons are in the tank after 10 minutes? Check the correct answer. _____ A.

330

_____ B.

1,250

_____ C.

2,500

_____ D.

3,300

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KeyTrain Applied Mathematics

Level 6 Rate Problems

Rates Problem 15 An assembly line produces 2 toasters per minute. It is 2:00 p.m., and the line has finished 560 out of its goal of 900 for the day. The line stops at 5:00 p.m. A coworker is urging you to stop the line for a half hour break, saying that you will make the goal anyway. Should you stop the line for a half hour break? Check the correct answer. _____ A.

Yes, you will beat the goal anyway.

_____ B.

No, you will be 40 toasters short if you do.

_____ C.

OK, you will have just enough.

_____ D.

Can’t tell from this information.

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Level 6 Rate Problems

Summary – Rate Problems Understanding rates is one of the keys to efficient planning. Using rates, you can predict how much product a company can produce and how much materials will be needed. You can determine if a person or team will be able to accomplish its job in time. Rates can be adjusted for different time periods. If you know how many parts can be made in an hour, then you can tell how many parts can be made in a week, month or year. Use this in your job to see how efficient your business is.

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Level 6 Best Deals

Level 6 Applied Mathematics Best Deals

Best Deal problems involve making comparisons between different options. The best deal is the option that fulfills the goal of the situation better. It may be the option that costs less, makes more money, or uses less energy. In the workplace, employees may often need to do several calculations to compare costs and then choose the best deal. In this section, the problems will involve several calculations to be able to determine the best option.

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Level 6 Best Deals

Solving Best Deal Problems Solving best deal problems involves several basic steps:

• Read the problem • Break the problem into smaller problems • Compute the different options • Compare each option and determine the best one. Here is an example: Power company A sells electricity for $0.04/kwhr (kilowatt hour). Company B sells for $0.03/kwhr plus a $100/month charge. If your business uses 4,000 kilowatt hours per month, which company should you use? Compute one company at a time: Company A: $0.04/kwhr x 4,000 kwhr = $160 Company B: ($0.03/kwhr x 4,000 kwhr) + $100 = $120 + $100 = $220

Company A will supply the required electricity for less.

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Level 6 Best Deals

Best Deals Problem 1 The next 10 problems will give you practice at determining the best deal. Each problem will show you two different prices for the same goods. Determine which is cheaper, or if they are the same.

Which is cheaper? Check the correct answer. _____ A.

1 liter of acetone for $9.75

_____ B.

32 liters of acetone for $184.64

_____ C.

They are the same.

Best Deals Problem 2 This problem will give you practice at determining the best deal. Below are two different prices for the same goods. Determine which is cheaper, or if they are the same.

Which is cheaper? Check the correct answer. _____ A.

58 copies for $5.80

_____ B.

12 copies for $1.32

_____ C.

They are the same.

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KeyTrain Applied Mathematics

Level 6 Best Deals

Best Deals Problem 3 This problem will give you practice at determining the best deal. Below are two different prices for the same goods. Determine which is cheaper, or if they are the same.

Which is cheaper? Check the correct answer. _____ A.

54 quarts of oil for $67.50

_____ B.

39 quarts of oil for $31.20

_____ C.

They are the same.

Best Deals Problem 4 This problem will give you practice at determining the best deal. Below are two different prices for the same goods. Determine which is cheaper, or if they are the same.

Which is cheaper? Check the correct answer. _____ A.

93 lbs. of hamburger for $267.84

_____ B.

67 lbs. of hamburger for $145.39

_____ C.

They are the same.

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KeyTrain Applied Mathematics

Level 6 Best Deals

Best Deals Problem 5 This problem will give you practice at determining the best deal. Below are two different prices for the same goods. Determine which is cheaper, or if they are the same.

Which is cheaper? Check the correct answer. _____ A.

8 boxes of pens for $30.00

_____ B.

36 boxes of pens for $86.40

_____ C.

They are the same.

Best Deals Problem 6 This problem will give you practice at determining the best deal. Below are two different prices for the same goods. Determine which is cheaper, or if they are the same.

Which is cheaper? Check the correct answer. _____ A.

89 boxes of labels for $1,566.40

_____ B.

14 boxes of labels for $385.00

_____ C.

They are the same.

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KeyTrain Applied Mathematics

Level 6 Best Deals

Best Deals Problem 7 This problem will give you practice at determining the best deal. Below are two different prices for the same goods. Determine which is cheaper, or if they are the same.

Which is cheaper? Check the correct answer. _____ A.

36 cans of tuna for $18.72

_____ B.

2 can of tuna for $1.86

_____ C.

They are the same.

Best Deals Problem 8 This problem will give you practice at determining the best deal. Below are two different prices for the same goods. Determine which is cheaper, or if they are the same.

Which is cheaper? Check the correct answer. _____ A.

9 gallons of gas for $12.42

_____ B.

67 gallons of gas for $64.32

_____ C.

They are the same.

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KeyTrain Applied Mathematics

Level 6 Best Deals

Best Deals Problem 9 This problem will give you practice at determining the best deal. Below are two different prices for the same goods. Determine which is cheaper, or if they are the same.

Which is cheaper? Check the correct answer. _____ A.

65 cases of paper for $1,267.50

_____ B.

92 cases of paper for $1,794.00

_____ C.

They are the same.

Best Deals Problem 10 This problem will give you practice at determining the best deal. Below are two different prices for the same goods. Determine which is cheaper, or if they are the same.

Which is cheaper? Check the correct answer. _____ A.

92 cases of soda for $330.28

_____ B.

40 cases of soda for $177.20

_____ C.

They are the same.

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KeyTrain Applied Mathematics

Level 6 Best Deals

Best Deals Problem 11 A printing business employs 35 people. The employer offers his employees an insurance package that costs him $2,170. He has been investigating various plans. A new plan would cost him $59 per employee plus a $70 sign up fee. Is the new plan a better deal? Check the correct answer. _____ A.

Yes

_____ B.

No

_____ C.

Not enough information

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KeyTrain Applied Mathematics

Level 6 Best Deals

Best Deals Problem 12 Your business is studying phone companies. Company A charges $12.50 per month plus $0.15 per minute for any call. Company B charges $14.95 per month plus $0.12 per minute for any call. You average 2 1/2 hours of calls each month. Which company is the better deal and how much will you save? Check the correct answer. _____ A.

Company A by $2.05 per month

_____ B.

Company B by $2.05 per month

_____ C.

Company A by $2.45 per month

_____ D.

Company B by $2.45 per month

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KeyTrain Applied Mathematics

Level 6 Best Deals

Best Deals Problem 13 You are fencing in a garden area for a client. She is unsure of what shape she wants but is debating between a circle or a square. She has purchased 50 feet of fencing to go around the garden. Your choices would be a circular garden with a diameter of 15.5 feet or a 12 1/2 foot square. Which shape most effectively uses the fencing already purchased? Check the correct answer. _____ A.

Square

_____ B.

Circle

_____ C.

Neither is better

_____ D.

Not enough information

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KeyTrain Applied Mathematics

Level 6 Best Deals

Best Deals Problem 14 A graduate is looking for a job. She has been offered two different jobs that she must decide between. One job pays $6.50 per hour plus an 8% commission on sales over $3,000. Her perspective employer guarantees that she will work 40 hours per week and should easily sell $6,000 worth of merchandise each week. The second job pays $7.25 per hour for a 40-hour week and a 5% commission on all sales. (Assume $5,000 worth of sales each week). Where would your annual salary be best? Check the correct answer. _____ A.

Job 1, $6.50 per hour

_____ B.

Job 2, $7.25 per hour

_____ C.

They have the same annual salary

_____ D.

There is not enough information

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KeyTrain Applied Mathematics

Level 6 Best Deals

Best Deals Problem 15 You inherit $5,000 from your uncle and want to invest the money. You go to two banks to find the best deal. Sunshine Bank suggests you invest the money in a Certificate of Deposit (CD) that earns 5% interest every six months. Moonlight Bank suggests that you purchase a stock that is currently paying 9% in annual dividends. You plan on investing the money for 5 years. Where will you get the best deal? Check the correct answer. _____ A.

Sunshine Bank

_____ B.

Moonlight Bank

_____ C.

They give the same return

_____ D.

There is not enough information

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KeyTrain Applied Mathematics

Level 6 Best Deals

Best Deals Problem 16 You are catering an anniversary party that is expecting 25 people. You plan on serving cake and punch. You may purchase these items from two different distributors. The first company will sell you a cake that serves 25 people for $25.95 and ingredients to make punch totaling $6.50. The second company charges $1.05 per person for cake and $0.25 per person for punch. Where will you get the best deal? Check the correct answer. _____ A.

First Company

_____ B.

Second Company

_____ C.

They are the same price

_____ D.

There is not enough information

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KeyTrain Applied Mathematics

Level 6 Best Deals

Summary – Best Deals Comparing different options to find the best deal can save you or your company money. Don't be afraid to shop around for a better deal! In each situation, compare the options:

• Determine the options • Break the options into smaller problems • Compute the different options • Compare each option and determine the best one.

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KeyTrain Applied Mathematics

Level 6 Answers

Level 6 Applied Mathematics Answers

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KeyTrain Applied Mathematics

Level 6 Multiple Steps - Answers

Multiple Steps – Answers Multiple Steps Problem 1: The correct answer is B. What is the problem asking? How much is spent? What are the facts? Earned $100 per week for 15 weeks Saved $35.75 per week Set up and solve the problem: Total earned = $100 × 15 = $1,500 Total saved = $35.75 × 15 = $536.25 He either saved or spent everything he earned, so Earned - Saved = Spent $1,500 - $536.25 = $963.75 Check your answer: $963.75 + $536.26 = $1,500.00

Multiple Steps Problem 2: The correct answer is D. What is the problem asking? How much sodium is in the meal? What are the facts? Using the table, she had: orange juice 4 mg corn flakes 251 mg milk 120 mg 2 toasts (170 mg x 2) 340 mg 2 butters (41 mg x 2) 82 mg coffee 0 mg Set up and solve the problem: Add the numbers above : 4 + 251 + 120 + 340 + 82 = 797 mg Check your answer: First, check your list to make sure everything is included, and then estimate.

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KeyTrain Applied Mathematics

Level 6 Multiple Steps - Answers

Multiple Steps Problem 3: The correct answer is A. What is the problem asking? How much sodium is in the meal? What are the facts? Using the table, she had: orange juice 4 mg bacon (2 slices/serving) 325 mg 3 eggs (50 x 3) 150 mg milk 120 mg 2 toasts (170 mg x 2) 340 mg 2 butters (41 mg x 2) 82 mg Set up and solve the problem: Add the numbers above : 4 + 325 + 150 + 120 + 340 + 82 = 1,021 mg Is total less than 1,100? Yes Check your answer: First, check your list to make sure everything is included, and then estimate.

Multiple Steps Problem 4: The correct answer is C. What is the problem asking? How many patients were left? What are the facts? Patients received (added) and discharged (subtracted) as shown. Set up and solve the problem: Can do it day by day or totals. If we do it day by day. Tuesday : 100 + 15 - 3 = 112 Wednesday : 112 + 9 - 12 = 109 Thursday : 109 + 5 - 2 = 112 Friday : 112 + 13 - 5 = 120 Check your answer: Check by totaling received and discharged: 100 + 42 – 22 = 120.

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KeyTrain Applied Mathematics

Level 6 Multiple Steps - Answers

Multiple Steps Problem 5: The correct answer is A. What is the problem asking? How much is left in the checking account? What are the facts? How much is left in the checking account: Original balance - $500 Payment 4 months - $35 Payment 3 months - $25 Set up and solve the problem: Payments = (4 × $35) + (3 × $25) = $215 Original - Payments = Balance $500 - $215 = $285

Multiple Steps Problem 6: The correct answer is A. What is the problem asking? The temperature at the end of the day What are the facts? Temperature rose 5 degrees Then it dropped 9 degrees The temperature in the morning was 3 degrees below zero Set up and solve the problem: Start with original temperature : - 3 degrees Temperature rose 5 degrees Temperature dropped 9 degrees Final temperature = - 3 + 5 - 9 = - 7 degrees

Multiple Steps Problem 7: The correct answer is D. What is the problem asking? What is the difference in the highest and lowest temperatures? What are the facts? Highest temperature in the 2 years was 38 Celsius. Lowest temperature in the 2 years was –25 degrees Celsius. Set up and solve the problem: Difference in the two temperatures is : 38 - (-25) = 38 + 25 = 63 C. Check your answer. Estimate as: 40 + 20 = 60 Similar

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Level 6 Multiple Steps - Answers

Multiple Steps Problem 8: The correct answer is C. What is the problem asking? Is your balance correct, and if not, what did you do wrong? What are the facts? Last balance of $463.76 Checks of $12.56, $52.11, $26.03 Deposits of $101.32, $10.98 Set up and solve the problem: Check balance again : $463.76 - $12.56 - $52.11 - $26.03 + $101.32 + $10.98 = $485.36 So bank OK. Difference in bank and your balance : $511.39 - $485.36 = $26.03 You forgot to subtract the $26.03 check.

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KeyTrain Applied Mathematics

Level 6 Fractions and Decimals - Answers

Fractions and Decimals – Answers Fractions and Decimals Problem 1: The correct answer is B. What is the problem asking? What is the weight of a one-foot section? What are the facts? 1 3 Bar measures 16 feet and Bar weighs 105 pounds 2 4 Set up and solve the problem: 3 105 pounds ? 4 = 1 1 foot 16 feet 2 Can convert to decimal : 105.75 ÷ 16.5 = 6.4 Or, use improper fractions : (105 × 4) + 3 (16 × 2) + 1 432 33 423 2 ÷ = ÷ = × = 6.4 4 2 4 2 4 33

Fractions and Decimals Problem 2: The correct answer is C. What is the problem asking? How much rod is needed for 15 drills? What are the facts? 1 Each drill is 4 inch long 16 5 Each drill requires inch waste 32 Set up and solve the problem: 1 5 Each drill needs 4 + 16 32 1 1 (4 × 16) + 1 65 Convert 4 to fraction : 4 = = 16 16 16 16 Find common denominator and add : 65 5 130 5 135 + = + = 16 32 32 32 32 Multiply by 15 drills : 135 2,025 9 15 × = = 63 inches 32 32 32

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Level 6 Fractions and Decimals - Answers

Fractions and Decimals Problem 3: The correct answer is C. What is the problem asking? Total length including holes. What are the facts? 3 Centers are 4 inches apart 8 3 Holes are inches in diameter 4 Set up and solve the problem:

diameter of hole is 3/4 inch

centers of holes are 4 3/8 inches apart 3 3 3 Distance is 4 × 4 inches + inches ( inch is for one half of hole on 8 4 4 each end of the last centers) 35 3 Convert 4 to 8 8

Multiply and add : 35 6 146 1 × 4 + = = 18 inches 8 8 8 4

Fractions and Decimals Problem 4: The correct answer is B. What is the problem asking? What is the number of square yards of carpet needed for a room and hallway? What are the facts? Room: 14 feet 6 inches by 22 feet 9 inches Hallway: 4 feet by 9 feet 8 inches Set up and solve the problem: Must multiply lengths to find the area. Need to convert to a single unit. (For example, convert to decimal feet.) Room : 14.5 ft. × 22.75 ft. = 330 sq. ft. Hall : 4 ft. × 9.67 ft. = 38.7 sq. ft. Total = 330 + 38.7 = 368.7 sq. ft. Convert to square yards by dividing by 9 : 368.7 ÷ 9 = 41 sq. yd.

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Level 6 Fractions and Decimals - Answers

Fractions and Decimals Problem 5: The correct answer is D. What is the problem asking? What is the total power used by appliances? What are the facts? 7 3 3 appliances with 1 watts and 2 appliances with 4 watts 8 4 Set up and solve the problem: 7 3 Total power = (3 × 1 ) + (2 × 4 ) 8 4 15 19 = (3 × ) + (2 × ) 8 4 45 38 (need common denominator) = + 4 8 45 + 76 121 1 = = = 15 watts 8 8 8

Fractions and Decimals Problem 6: The correct answer is C. What is the problem asking? How many links must be used to make the chain? What are the facts? Total length - - 15 inches 1 1 Each link - - inch; clasp inch 4 2 Set up and solve the problem: First, subtract the clasp to determine the length of the chain links : 1 1 15 inches - inch = 14 inches 2 2 In order to determine the toal number of links, you need to divide the total by each link : 1 1 14 inches ÷ = ? (to divide, invert and then multiply) 2 4 1 14 × 4 = 14.5 × 4 = 58 links. 2

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Level 6 Fractions and Decimals - Answers

Fractions and Decimals Problem 7: The correct answer is C. What is the problem asking? Is the shipping weight wrong, and if so, why? What are the facts? 12 gears at 1 lb. 3 oz. each Box weighs 2 lbs. Marked as 15.6 lbs. Set up and solve the problem: 3 1 lb. 3 oz. = 1 lb. + ( lb.) = 1.19 (16 ounces in a pound) 16 Weight = 12 × 1.19 lbs. + 2 lbs. = 16.3 lbs. If he missed the box, the weight would have been 14.3 lbs. If he had only counted 10 gears, the weight would be 13.9 lbs. The conversion must be wrong (He actually assumed 1 lb. 3 oz. equaled 1.3 lbs.)

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KeyTrain Applied Mathematics

Level 6 Percentages - Answers

Percentages – Answers Percentages Problem 1: The correct answer is 18%. 163 ÷ 921.5 = 0.176 (round to 0.18) which become 18%

Percentages Problem 2: The correct answer is 76%. 516.5 ÷ 675.7 = 0.764 (round to 0.76) which become 76%

Percentages Problem 3: The correct answer is 48%. 325.7 ÷ 678.3 = 0.480 (round to 0.48) which become 48%

Percentages Problem 4: The correct answer is 58%. 157.8 ÷ 273 = 0.578 (round to 0.58) which become 58%

Percentages Problem 5: The correct answer is 36%. 269.2 ÷ 744.9 = 0.361 (round to 0.36) which become 36%

Percentages Problem 6: The correct answer is 3%. 24.3 ÷ 695.7 = 0.034 (round to 0.03) which become 3%

Percentages Problem 7: The correct answer is 46%. 300.2 ÷ 656.4 = 0.457 (round to 0.46) which become 46%

Percentages Problem 8: The correct answer is 58%. 35.4 ÷ 61.4 = 0.576 (round to 0.58) which become 58%

Percentages Problem 9: The correct answer is 59%. 582.1 ÷ 990.2 = 0.587 (round to 0.59) which become 59%

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Level 6 Percentages - Answers

Percentages Problem 10: The correct answer is 51%. 301.5 ÷ 593.2 = 0.508 (round to 0.51) which become 51%

Percentages Problem 11: The correct answer is 366. X × 34% = X × 0.34 = 124.44; so 124.44 ÷ 0.34 = 366

Percentages Problem 12: The correct answer is 283. X × 4% = X × 0.04 = 11.32; so 11.32 ÷ 0.04 = 283

Percentages Problem 13: The correct answer is 971. X × 30% = X × 0.30 = 291.3; so 291.3 ÷ 0.30 = 971

Percentages Problem 14: The correct answer is 222. X × 33% = X × 0.33 = 73.26; so 73.26 ÷ 0.33 = 222

Percentages Problem 15: The correct answer is 72. X × 25% = X × 0.25 = 18; so 18 ÷ 0.25 = 72

Percentages Problem 16: The correct answer is 190. X × 37% = X × 0.37 = 70.3; so 70.3 ÷ 0.37 = 190

Percentages Problem 17: The correct answer is 38. X × 24% = X × 0.24 = 9.12; so 9.12 ÷ 0.24 = 38

Percentages Problem 18: The correct answer is 13. X × 17% = X × 0.17 = 2.21; so 2.21 ÷ 0.17 = 13

Percentages Problem 19: The correct answer is 927. X × 43% = X × 0.43 = 398.61; so 398.61 ÷ 0.43 = 927

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Level 6 Percentages - Answers

Percentages Problem 20: The correct answer is 715. X × 62% = X × 0.62 = 443.3; so 443.3 ÷ 0.62 = 715

Percentages Problem 21: The correct answer is D. What is the problem asking? How many homes are there in total? What are the facts? 25% have computers 50 homes have computers Set up and solve the problem: Use a ratio : 50 25 = (percentage out of 100) ? 100

? = 100 × 50 ÷ 25 = 200 OR divide number by the percent : ? = 50 ÷ 0.25 = 200

Percentages Problem 22: The correct answer is 68%. Amount of change = 1,031.52 - 614 = 417.52 417.52 × 100% = 0.68 × 100% = 68% Percent increase = 614

Percentages Problem 23: The correct answer is 31%. Amount of change = 451.95 - 345 = 106.95 106.95 × 100% = 0.31 × 100% = 31% Percent increase = 345

Percentages Problem 24: The correct answer is 39%. Amount of change = 706.12 - 508 = 198.12 198.12 × 100% = 0.39 × 100% = 39% Percent increase = 508

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Level 6 Percentages - Answers

Percentages Problem 25: The correct answer is 64%. Amount of change = 1,382.52 - 843 = 539.52 539.52 × 100% = 0.64 × 100% = 64% Percent increase = 843

Percentages Problem 26: The correct answer is 94%. Amount of change = 1,627.66 - 839 = 788.66 788.66 × 100% = 0.94 × 100% = 94% Percent increase = 839

Percentages Problem 27: The correct answer is 45%. Amount of change = 255 - 140.25 = 114.75 114.75 × 100% = 0.45 × 100% = 45% Percent decrease = 255

Percentages Problem 28: The correct answer is 25%. Amount of change = 592 - 444 = 148 148 × 100% = 0.25 × 100% = 25% Percent decrease = 592

Percentages Problem 29: The correct answer is 90%. Amount of change = 1,618.8 - 852 = 766.8 766.8 × 100% = 0.90 × 100% = 90% Percent increase = 852

Percentages Problem 30: The correct answer is 4%. Amount of change = 11.44 - 11 = 0.44 0.44 × 100% = 0.04 × 100% = 4% Percent increase = 11

Percentages Problem 31: The correct answer is 96%. Amount of change = 423 - 16.92 = 406.98 406.98 × 100% = 0.96 × 100% = 96% Percent decrease = 423

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Level 6 Percentages - Answers

Percentages Problem 32: The correct answer is C. What is the problem asking? How many customers used a credit card? What are the facts? 75% of customers paid with credit cards There were a total of 50 customers that day Write and solve the problem: Need to find 75% of 50 customers 75% x 50 = 0.75 x 50 = 37.5 (round up to 38) Check your answer: 3 38 is about (75%) of 50. 4

Percentages Problem 33: The correct answer is D. What is the problem asking? What was the original purchase price of the shares of stock? What are the facts? Profit = $1,320 Profit was 15% (days does not matter) Write and solve the problem: 15% = $1,320 100% = ? Can use a ratio : $1,320 15 = 100 X 15X = 1320 × 100 X = 132000 ÷ 15 = $8,800 OR 1320 = $8,800 0.15 Check your answer: $8,800 × 15% = $8,800 × 0.15 = $1,320

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Level 6 Percentages - Answers

Percentages Problem 34: The correct answer is A. What is the problem asking? What is the percent of decrease in attendance? What are the facts? 1st event attendance was 250 2nd event attendance was 230 Write and solve the problem: Amount decrease = 250 - 230 = 20 amount decrease 20 Percent decrease = = = 0.08 250 original amount = 20 ÷ 250 × 100% = 0.08 × 100% = 8% Check your answer: 250 × 8% = 20 = decrease amount

Percentages Problem 35: The correct answer is D. What is the problem asking? What is the original price and sale price? What are the facts? Amount saved -- $12.50 Jeans were 25% off original price Write and solve the problem: 25% = $12.50 Use ratio : 25 $12.50 = 100 n (original price) 25n = $1250.00 n = $50 (original price) Sale price = $50 - $12.50 = $37.50 Check your answer: $50 × 25% = $12.50 OK

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Level 6 Percentages - Answers

Percentages Problem 36: The correct answer is B. What is the problem asking? What is the selling price? What are the facts? Cost -- $155 Marked price was 30% above cost Sold for 10% less than marked price Write and solve the problem: Original Cost = $155 Marked Price = $155 + (30% × $155) = $155 + (0.30 × $155) = $201.50 Sold for = $201.50 - (10% × $201.50) = $201.50 - (0.10 × $201.50) = $181.35 Check your answer: Check the math again.

Percentages Problem 37: The correct answer is B. What is the problem asking? What is the profit made by the owner? What are the facts? Sold for -- $181.35 Original cost -- $155 Write and solve the problem: Amount increase = $181.35 - $155 = $26.35 amount increase $26.35 Ratio = = = 0.17 original cost $155 Percent increase = .17 × 100 = 17% Check your answer: $155 × 17% = $26.35 OK

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KeyTrain Applied Mathematics

Level 6 Percentages - Answers

Percentages Problem 38: The correct answer is C. What is the problem asking? Total earnings for the week What are the facts? Base pay -- $250 per week 3% commission on sales over $5,000 Total weekly sales -- $9,525 Write and solve the problem: Total Pay = Base + Commission Commission = 3% of sales over $5,000 = 3% × ($9,525 - $5,000) = 3% × $4,525 = 0.03 × $4,525 = $135.75 Total Pay = $250 + $135.75 = $385.75 Check your answer: Check math again.

Percentages Problem 39: The correct answer is D. What is the problem asking? Is the price right? If not, why? What are the facts? MSRP = $180 Normal price 20% off Sale 30% off normal price Write and solve the problem: Normal price = $180 - ($180 × 0.20) = $144.00 Sale price = $144 - ($144 × 0.30) = $100.80 By trial and error, 30% off MSRP = $126, not $90 But if you subtracted 30% of MSRP $144 - ($180 × 0.30) = $90

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KeyTrain Applied Mathematics

Level 6 Area and Volume - Answers

Area and Volume – Answers Area and Volume Problem 1: The correct answer is 50.41 square yards. Area = length x width = 7.1 yds. x 7.1 yds. = 50.41 sq. yds.

Area and Volume Problem 2: The correct answer is 67.2 feet. Perimeter = (2 x length) + (2 x width) = (2 x 16.8 ft.) + (2 x 16.8 ft.) = 67.2 ft.

Area and Volume Problem 3: The correct answer is 392.04 square meters. Area = length x width = 19.8 m. x 19.8 m. = 392.04 sq. m.

Area and Volume Problem 4: The correct answer is 124.63 square inches. 1 Area = π r 2 r = diameter = 12.6 ft. ÷ 2 = 6.3 in. 2 Area = 3.14 × 6.3 ft. × 6.3 in. = 124.626 sq. in. (round to 124.63 sq. in.)

Area and Volume Problem 5: The correct answer is 3.80 square inches. 1 2.2 d = 2.2 ft. r = diameter = = 1.1 ft. 2 2 Area = π r 2 = 3.14 × 1.1 ft. × 1.1 ft. = 3.7994 (rounded to 3.80 sq. ft.)

Area and Volume Problem 6: The correct answer is 121.2 yards. 1 Circumference = π × d r = diameter, so diameter = 2 × r = 2 × 19.3 yds. = 38.6 yds . 2 Circumference = 3.14 × 38.6 = 121.204 yards (rounded to 121.20 yards)

Area and Volume Problem 7: The correct answer is 40.82 feet. 1 Circumference = π × d r = diameter, so diameter = 2 × r = 2 × 6.5 ft. = 13 ft. 2 Circumferencre = 3.14 × 13 = 40.82 feet

Area and Volume Problem 8: The correct answer is 46.2 inches. Perimeter = (2 x length) + (2 x width) = (2 x 19.1 in.) + (2 x 4 in.) = 46.2 inches Copyright © 2000, SAI Interactive, Inc. For use only by Chicago Public Schools. Page 149

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Level 6 Area and Volume - Answers

Area and Volume Problem 9: The correct answer is 13.6 square inches. Area = length x width = 3.4 in. x 4 in. = 13.6 sq. in.

Area and Volume Problem 10: The correct answer is 30.6 feet. Perimeter = (2 x length) + (2 x width) = (2 x 5.5 ft.) + (2 x 9.8 ft.) = 30.6 feet

Area and Volume Problem 11: The correct answer is D. What is the problem asking? What is the volume of the toolbox? What are the facts? Length = 1 foot Width = 6 inches Height = 8 inches Set up and solve the problem: Make sure the units of measurement are the same : volume = length × width × height volume = 12 inches × 6 inches × 8 inches = 576 cubic inches

Area and Volume Problem 12: The correct answer is B. What is the problem asking? What is the length of the parcel? What are the facts? Area = 2 square miles Width = 6,500 feet Set up and solve the problem: Make sure the units of measurement are the same : Convert width to miles (1 mile = 5,280 feet) 6,500 ft. width = = 1.231 miles 5,280 ft./mile Length = area ÷ width = 2 sq. mi. ÷ 1.231 mi. = 1.625 mi. Convert length back to feet : 1.625 × 5,280 = 8,580 feet

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Level 6 Area and Volume - Answers

Area and Volume Problem 13: The correct answer is C. What is the problem asking? What is the cost of the flooring? What are the facts? Floor: 16 feet by 14 feet 6 inches Cost: $18.50 per sq. ft. Set up and solve the problem: Area = length × width = 16 ft. × 14 ft. 6 in. = 16 ft. × 14.5 ft. (convert to common units) = 232 sq. ft. Total Cost = area × cost per square foot = 232 sq. ft. × $18.50 per sq. ft. = $4,292

Area and Volume Problem 14: The correct answer is B. What is the problem asking? How many cubic feet of concrete are needed for a sidewalk? What are the facts? Space: length – 10 feet; width – 3 feet; thickness – 6 inches Set up and solve the problem: Cubic feet implies volume; and you need to convert the values to the same unit volume = length × width × height = 10 ft. × 3 ft. × .5 ft. (converted 6 inches to .5 feet) = 15 cubic feet

Area and Volume Problem 15: The correct answer is C. What is the problem asking? What is the square feet remaining uncovered? What are the facts? Floor: Area = 238 sq. ft. Rug: 9 ft. by 12 ft. Set up and solve the problem: Remaining Area = Floor Area - Rug Area = 238 sq. ft. - (9 ft. × 12ft.) = 238 sq. ft. - 108 sq. ft = 130 sq ft. of remaining area

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KeyTrain Applied Mathematics

Level 6 Area and Volume - Answers

Area and Volume Problem 16: The correct answer is A. What is the problem asking? What is the area of the tablecloth? What are the facts? Length = 41 inches Width = 25 inches 1 square foot = 144 square inches (from the conversion table) Set up and solve the problem: Area of Rectangular table = 41 in. × 25 in. = 1,025 square inches 1,025 sq. in. Area = = 7.1 sq. ft. 144 sq. in./sq. ft.

Area and Volume Problem 17: The correct answer is B. What is the problem asking? How many cubic meters are in the aquarium? What are the facts? Facts: length = 4 meters; width = 2 meters; height = 3 meters Set up and solve the problem: Volume = length × width × height = 4 m. × 2 m. × 3 m. = 24 cubic meters

Area and Volume Problem 18: The correct answer is C. What is the problem asking? How many square feet of carpet are needed? What are the facts? Entry: 10 ft. by 9 ft. Living Room: 24 ft. by 18 ft. Carpet 90% of the total area Set up and solve the problem: Compute area of each room : Entry area = length × width = 10 ft. × 9 ft. = 90 sq. ft. Living Room area = length × width = 24 ft. × 18 ft. = 432 sq. ft. Total Area = entry area + living room area = 90 sq. ft. + 432 sq. ft. = 522 sq. ft. 90% of total area is the be carpeted : 522 sq. ft. × 90% = 522 sq. ft. × 0.90 = 469.8 (round up to 470)

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Level 6 Area and Volume - Answers

Area and Volume Problem 19: The correct answer is B. What is the problem asking? What is the cost of seeding the lawn? What are the facts? Lawn measures 15 yards by 12 yards 1 pound of seed costs $4.65 1 pound of seed covers 135 square feet 1 yard = 3 feet Set up and solve the problem: 15 yards = 15 × 3 ft. = 45 ft. 12 yards = 12 × 3 ft. = 36 ft. Area = 45 ft. × 36 ft. = 1,620 sq. ft. Use ratio for coverage (1 lb. covers 135 sq. ft.) : 1 lb. n lbs. = 135 sq. ft. 1,620 sq. ft. n = 1,620 ÷ 135 = 12 lbs. Cost = number of lbs. × price per lb. = 12 × $4.65 = $55.80

Area and Volume Problem 20: The correct answer is B. What is the problem asking? How many bins are needed? What are the facts? Dimensions: 6 meters by 3 meters by 5.4 meters There are 100 cubic meters to be stored Set up and solve the problem: Volume of one bin = length × width × height = 6 m. × 3 m. × 5.4 m. = 97.2 cubic meters So 2 bins will hold 100 cubic meters (97.2 × 2 = 194.4 cubic meters)

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Level 6 Area and Volume - Answers

Area and Volume Problem 21: The correct answer is C. What is the problem asking? How much does the cellar cost? What are the facts? 36 feet long, 14 feet wide, 8 ft. deep $5.90 per cubic yard digging $20 per square foot finishing Set up and solve the problem: Digging is based on volume. Finishing is based on area. Volume = length × width × height (or depth) = 36 ft. × 14 ft. × 8 ft. = 4,032 cu. ft. = 149.3 cu. yd. (divided by 27) Area = length × width = 36 ft. × 14 ft. = 504 sq. ft. Cost = (149.3 cu. yd. × $5.90 per cu. yd.) + (504 sq. ft. × $20 per sq. ft.) = $10,960.87

Area and Volume Problem 22: The correct answer is B. What is the problem asking? How much concrete is needed for the driveway? What are the facts? Facts: length – 81 ft.; width – 12 ft.; height (depth) – 6 inches Set up and solve the problem: Volume = length × width × height (or depth) = 81 ft. × 12 ft. × 0.5 ft. (converted inches to ft.) = 486 cu. ft.

Area and Volume Problem 23: The correct answer is D. What is the problem asking? Weight of an ice block What are the facts? Facts: length – 1.5 ft.; width – 1.5 ft.; height (depth) – 1.5 ft. Weight: 57 pounds per cubic foot Set up and solve the problem: Volume = length × width × height (or depth) = 1.5 ft. × 1.5 ft. × 1.5 ft. = 3.375 cu. ft. Weight = number of cubic feet × 57 lbs. per cubic foot = 192.375 lbs.

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Level 6 Area and Volume - Answers

Area and Volume Problem 24: The correct answer is A. What is the problem asking? Which figure has the greater volume? What are the facts? Cube: 6 centimeters on each side Rectangle: 3 centimeters square base and 12 centimeter height Set up and solve the problem: Cube Volume = length × width × height = 6 cm. × 6 cm. × 6 cm. = 216 cubic centimeters Rectangle Volume = length × width × height = 3 cm. × 3 cm. × 12 cm. = 108 cubic centimeters The cube is larger

Area and Volume Problem 25: The correct answer is A. What is the problem asking? Is the volume right? If not, why? What are the facts? Size is 5 feet 3 inches by 3 feet 6 inches by 4 feet 9 inches Marked as 87.3 cubic feet Set up and solve the problem: Calcuate Volume = length × width × height (convert inches to feet) 3 5'3" = 5 + = 5.25 ft. 12 6 = 3.5 ft. 3'6" = 3 + 12 9 = 4.75 ft. 4'9" = 4 + 12 Volume = 5.25 ft. × 3.5 ft. × 4.75 ft. = 87.28 (rounded to 87.3 cubic feet) The volume is correctly marked.

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Level 6 Rate Problems - Answers

Rate Problems – Answers Rates Problem 1: The correct answer is 1.53 cases per hour. 68.9 cases = 68.9 cases ÷ 45 hours = 1.53 cases per hour 45 hours

Rates Problem 2: The correct answer is 0.7 inches per second. 14 inches = 14 inches ÷ 20 seconds = 0.7 inches per second 20 seconds

Rates Problem 3: The correct answer is 0.39 yards per minute. 8.5 yards = 8.5 yards ÷ 22 minutes = 0.386 (rounded to 0.39 yards per minute) 22 minutes

Rates Problem 4: The correct answer is 1.71 meters per second. 92.5 meters = 92.5 meters ÷ 54 seconds = 1.71 meters per second 54 seconds

Rates Problem 5: The correct answer is 1.35 sections per meter. 66.2 sections = 66.2 sections ÷ 49 meters = 1.35 sections per meter 49 meters

Rates Problem 6: The correct answer is 1.10 parts per shift 69.2 parts = 69.2 parts ÷ 63 shifts = 1.098 (rounded to 1.10 parts per shift) 63 shifts

Rates Problem 7: The correct answer is 1.81 miles per hour. 86.9 miles = 86.9 miles ÷ 48 hours = 1.81 miles per hour 48 hours

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Level 6 Rate Problems - Answers

Rates Problem 8: The correct answer is 1.53 dollars per ton. 68.8 dollars = 68.8 dollars ÷ 45 tons = 1.528 (rounded to 1.53 dollars per ton) 45 tons

Rates Problem 9: The correct answer is 0.06 kilometers per hour. 5.5 kilometers = 5.5 kilometers ÷ 90 hours = 0.06 kilometers per hour 90 hours

Rates Problem 10: The correct answer is 1.53 dollars per hour. 96.3 dollars = 96.3 dollars ÷ 63 hours = 1.528 (rounded to 1.53 dollars per hour) 63 hours

Rates Problem 11: The correct answer is C. What is the problem asking? How many words are typed in a week? What are the facts? 79 word per minute 5 days 8 hours each day Set up and solve the problem: Total Time = 5 days × 8 hours/day × 60 minutes/hour = 2,400 minutes Total Words = 2,400 minutes × 79 word/minute = 189,600 words

Rates Problem 12: The correct answer is D. What is the problem asking? How many total gallons are pumped? What are the facts? Pump 1 -- 60 gallons per minute Pump 2 -- 50 gallons per minute Two pumps for 30 minutes Set up and solve the problem: Pump 1 = 60 gpm × 30 minutes = 1,800 gallons Pump 2 = 50 gpm × 30 minutes = 1,500 gallons Total Gallons = 1,800 + 1,500 = 3,300 gallons

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Level 6 Rate Problems - Answers

Rates Problem 13: The correct answer is D. What is the problem asking? How much material is needed for a year? What are the facts? 1 dress – 2.5 yards of material Can produce 52 dresses each week; 1 year = 52 weeks Set up and solve the problem: Total Dresses = 52 dresses/week × 52 weeks/year = 2,704 dresses/year Amount of Material = 2,704 dresses/year × 2.5 yards/dress = 6,760 yards of material

Rates Problem 14: The correct answer is B. What is the problem asking? How many gallons are left in the tank? What are the facts? Pump 1 -- 125 gallons per minute into the tank Pump 2 -- 100 gallons per minute out of the tank Time = 10 minutes Initial Volume = 1,000 gallons Set up and solve the problem: Pump 1 = 125 gpm × 10 minutes = 1,250 gallons in (in means add) Pump 2 = 100 gpm × 10 minutes = 1,000 gallons out (out means subtract) Final Volume = initial volume + pump 1 gallons in - pump 2gallons out = 1,000 + 1,250 - 1,000 = 1,250 gallons

Rates Problem 15: The correct answer is B. What is the problem asking? Can you make the goal and still take a break? What are the facts? Make 2 toasters per minute Goal: 900 toasters; already made 560 toasters Time: 3 hours (2:00 p.m. – 5:00 p.m.) Set up and solve the problem: Rate = 2 toasters per minute × 60 minutes per hours = 120 toasters per hour Amount Needed = 900 - 560 = 340 toasters If you take a half hour break, production will run for 2.5 hours more 120 toasters/hour × 2.5 hours = 300 toasters You need to make 340 toasters. No, you cannot make the goal and still take a break. You will be 40 toasters short.

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KeyTrain Applied Mathematics

Level 6 Best Deals - Answers

Best Deals – Answers Best Deals Problem 1: The correct answer is B. $9.75 ÷ 1 liter = $9.75 per liter of acetone $184.64 ÷ 32 liters = $5.77 per liter of acetone

Best Deals Problem 2: The correct answer is A. $5.80 ÷ 58 copies = $0.10 per copy $1.32 ÷ 11 copies = $0.11 per copy

Best Deals Problem 3: The correct answer is B. $67.50 ÷ 54 quarts = $1.25 per quart of oil $31.20 ÷ 39 quarts = $0.80 per quart of oil

Best Deals Problem 4: The correct answer is B. $267.84 ÷ 93 lbs. = $2.88 per pound of hamburger $145.39 ÷ 67 lbs. = $2.17 per pound of hamburger

Best Deals Problem 5: The correct answer is B. $30.00 ÷ 8 boxes = $3.75 per box of pens $86.40 ÷ 36 boxes = $2.40 per box of pens

Best Deals Problem 6: The correct answer is A. $1,566.40 ÷ 89 boxes = $17.60 per box of labels $385.00 ÷ 14 boxes = $27.50 per box of labels

Best Deals Problem 7: The correct answer is A. $18.72 ÷ 36 cans = $0.52 per can of tuna $1.86 ÷ 2 cans = $0.93 per can of tuna

Best Deals Problem 8: The correct answer is B. $12.42 ÷ 9 gallons = $1.38 per gallon of gas $64.32 ÷ 67 gallons = $0.96 per gallon of gas

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Level 6 Best Deals - Answers

Best Deals Problem 9: The correct answer is C. $1,267.50 ÷ 65 cases = $19.50 per case of paper $1,794.00 ÷ 92 cases = $19.50 per case of paper

Best Deals Problem 10: The correct answer is A. $330.28 ÷ 92 cases = $3.59 per case of soda $177.20 ÷ 40 cases = $4.43 per case of soda

Best Deals Problem 11: The correct answer is A. What is the problem asking? Which insurance plan is a better deal? What are the facts? Employees – 35 Current Plan cost -- $2,170 New Plan cost == $59/employee + $70 Write and solve the problem: New Plan: ($59 x 35) + $70 = $2,135 Compare this to the current cost of $2,170. The new plan is the best deal.

Best Deals Problem 12: The correct answer is B. What is the problem asking? What is the total cost for each company? What are the facts? Company A -- $12.50/month + $0.15/minute Company B -- $14.95/month + $0.12/minute You use 2.5 hours per month Write and solve the problem: 2.5 hours = (60 x 2) + 30 = 150 minutes Company A: $12.50 + (150 x $0.15) = $35.00 Company B: $14.95 + (150 x $0.12) = $32.95 Company B is a better deal. The difference in cost is: $35.00 - $32.95 = $2.05 per month

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KeyTrain Applied Mathematics

Level 6 Best Deals - Answers

Best Deals Problem 13: The correct answer is A. What is the problem asking? Which shape uses the purchased fencing best? What are the facts? Purchased 50 feet fencing Circular garden -- 15.5 ft. diameter Square garden – 12.4 ft. length per side Write and solve the problem: Compute the length around each option : Circle : length = circumference = π × d (where d = diameter) = 3.14 × 15.5 ft. = 48.87 ft. Square : length = 4 × each side = 4 × 12.5 = 50 ft. The square shape will use all the purchased fencing.

Best Deals Problem 14: The correct answer is B. What is the problem asking? Which job would give the best annual salary? What are the facts? Job 1 -- $6.50 per hour; sales of $6,000 per week with an 8% commission on sales over $3,000 Job 2 -- $7.25 per hour; sales of $5,000 per week with a 5% on all sales 40 hours per week Write and solve the problem: Job 1 = ($6.50 × 40) + (8% × $3,000) = $260 + (0.08 × $3,000) = $260 + $240 = $500.00 Job 2 = ($7.25 × 40) + (5% × $5,000) = $290 + (0.05 × $5,000) = $290 + $250 = $540.00

Best Deals Problem 15: The correct answer is D. What is the problem asking? Which investment is better What are the facts? Sunshine Bank – 5% interest every 6 months Moonlight Bank – 9% annual dividends Write and solve the problem: This problem cannot be evaluated because interest rates fluctuate with time.

Best Deals Problem 16: The correct answer is A. What is the problem asking? Which company is giving the better deal? Copyright © 2000, SAI Interactive, Inc. For use only by Chicago Public Schools. Page 161

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Level 6 Best Deals - Answers

What are the facts? First company -- cake $25.95 for 25; punch $6.50 for 25 Second company – cake $1.05 per person; punch $0.25 per person Serving 25 people Write and solve the problem: Compare the total cost for each company : 1st company : $25.95 + $6.50 = $32.45 2nd company : ($1.05 × 25) + ($0.25 × 25) = $26.25 + $6.25 = $32.50 The first company offer a better deal by $0.05.

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