1 David & Claire is a retail shop selling fashion clothes for men and women.
David needs to arrange a number of clothes rails on the shop floor. Each clothes rail takes up a rectangular area of the floor of dimensions 3 m by 1 m.
3m Clothes rail
1m
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Retail – The Clothes Shop
(a) Work out the greatest number of clothes rails that David can arrange on the shop floor, which is in the shape of a rectangle of dimensions 13 m by 10 m.
There must always be at least one metre of space around each clothes rail and at least two metres between clothes rails. Show your arrangement in a diagram. 13 m
Shop floor
10 m
A maximum of 30 items can be hung on each clothes rail. An order of 150 dresses, 90 blouses, 120 jackets and 270 pairs of trousers has just been delivered. One clothes rail is to be filled with dresses, one with blouses, one with jackets and one with trousers. (b) (i) What fraction of the 150 dresses are put on a clothes rail?
(ii) What fraction of the 120 jackets will not be put on a clothes rail?
(c) How many more clothes rails would be needed to hang all of these clothes?
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Retail – The Clothes Shop
2 The delivery of clothes in question 1 arrived in some boxes.
Angela unpacks _2 of the boxes. Mason unpacks _ 5 of the boxes.
Emma unpacks the remaining boxes.
1
2
(a) What fraction of the boxes does Emma unpack? (b) If Mason unpacks 20 boxes, how many boxes were delivered? (c) Angela thinks 21 boxes were delivered. If everyone only unpacked whole boxes, why is she incorrect? Each box is a cuboid with dimensions 1 m by 0.8 m by 0.6 m. The boxes come in crates with dimensions 8 m by 3 m by 3.6 m.
3.6 m Crate Box 1m
0.6 m 0.8 m
3m 8m
(d) Work out the greatest number of boxes that can fit into one crate. The delivery company would like to use crates large enough to hold 250 boxes. (e) Design a crate that could be used to hold up to 250 boxes.
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Retail – The Clothes Shop
3 David & Claire employ nine staff: five men and four women. The men work in the Men’s department and the women work in the Women’s department. They each have a one-hour lunch break which must be taken between 12 00 and 14 00. The diagram shows the lunch break rota.
(a) Which staff are at lunch at: (i) 12 20 (ii) 13 40? (b) How many men are on lunch between 12 30 and 13 00? (c) How many women are working between 13 00 and 13 30? Claire says that there must be at least two women and at least two men working in the shop at all times. (d) Change the above lunch rota to ensure that there are at least two women and at least two men working in the shop at all times.
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Retail – The Clothes Shop
4 The diagrams are of print-outs from the tills in each department, showing the sales made on one day from 13 00 to 14 00. Each member of staff is shown on the print-out with a letter showing each individual sale.
For example,
A ……… £17.99 shows that John made a sale of £17.99,
B ……… £24.50 shows that Mohammed made a sale of £24.50.
A
John
B
Mohammed
C
Angela
D
Samantha
E
Zach
F
Mason
G
Nina
H
Emma
I
Finlay
(a) Who made the greatest number of sales? (b) Who took the greatest amount of money? (c) Calculate the mean sale for the men’s department and for the women’s department. Comment on these results. (d) Each staff member is paid commission at a rate of 2 per cent of the money they take for each sale. How much commission is Samantha paid for her sales between 13 00 and 14 00 on this day? Give your answer correct to the nearest penny. (e) Work out the amount taken by Zach and Mason as a percentage of the total takings for the men’s department. Give your answer to the nearest one per cent.
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Retail – The Clothes Shop
5 The pie charts show the percentage of sales in each of the departments for October and November. October
Women’s department 45%
55%
Men’s department
November
57%
43%
Women’s department Men’s department
(a) Half of the total sales in the men’s department in October were accessories. What percentage of the overall October sales were not men’s accessories? (b) Claire says that over these two months the women’s department has taken more money than the men’s department.
16
Give an example to show that this may not be true.
Retail – The Clothes Shop
6 In the men’s department, Finlay has 54 T-shirts to sell in a sale. The normal price of each T-shirt is £12. (a) How much money would be taken if Finlay sold all of these T-shirts for £12 each? David tells Finlay that, in the sale, his target is £500 for selling all 54 T-shirts. Finlay decides upon a special offer for selling these T-shirts. The special offer is: ‘Buy one T-shirt for £12 and get the second at half price’. (b) Finlay sells all of the T-shirts. Does he make his target? You must explain your answer fully.
(c) Describe a better offer that Finlay could have used to sell these T-shirts and meet his target of £500. In the women’s department sale, Nina has 12 dresses to sell. The normal price of each dress is £39.55. Nina’s target is £270. (d) What is the lowest price in the sale each of these dresses can be if Nina is to meet her target? (e) In the sale, Nina sells the dresses for £29.99 each. How many dresses must she sell to meet her target?
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Retail – The Clothes Shop
7 The Men’s Department
Make sure you write down all of your working and answers clearly.
These tables show the sales figures for men’s clothing for the trading year 2007–08, by size and value and by size and quantity.
Men’s sales (£)
18
January
February
March
April
May
June
Small
25 000
23 555
30 250
12 531
30 000
32 000
Medium
75 005
72 005
100 021
36 024
96 000
99 021
Large
65 127
57 622
62 277
21 001
73 500
55 487
July
August
September
October
November
December
Small
25 012
25 036
65 455
36 001
26 523
59 875
Medium
78 564
82 154
78 524
118 235
85 478
83 824
Large
55 077
61 007
89 565
92 329
67 734
95 799
Men’s sales (quantities) January
February
March
April
May
June
Small
1000
800
1212
1239
1200
3960
Medium
2356
2954
4568
5465
3840
3960
Large
3510
3521
3351
3521
3521
2658
July
August
September
October
November
December
Small
950
984
2654
1500
1060
2218
Medium
3142
3286
3140
4729
3419
3942
Large
3501
3541
2546
2399
2541
3000
Retail – The Clothes Shop
Fifty-seven per cent of total store sales were in ladies’ wear.
Ladies’ garments are purchased in the ratio: (Size 10–12 : Size 14–16 : Size 18–20) as (2 : 3 : 2). (a) Suggest and justify the ratio in which men’s garments should be purchased. (b) Is there a trend in the the total quantity of items sold over the year? (c) Construct a graph to illustrate sales (£) for the year. Comment on what your graph tells you. (d) Which month do you think there was a sale and why?
