ExpertMedium5 marksStructured
AQA GCSE · Question 06 · Ratio Proportion and Rates of Change
Three shops sell shirts. At which shop is it cheapest to buy 6 shirts? Show working to support your answer.
Shop A: Pack of 2, £19.00
Shop B: Was £12.40, Now 25% off (price per shirt)
Shop C: Pack of 3, £37.40. Buy one pack, get another pack half price.
Three shops sell shirts. At which shop is it cheapest to buy 6 shirts? Show working to support your answer.
Shop A: Pack of 2, £19.00
Shop B: Was £12.40, Now 25% off (price per shirt)
Shop C: Pack of 3, £37.40. Buy one pack, get another pack half price.
How to approach this question
1. For each shop, calculate the total cost to buy exactly 6 shirts.
2. **Shop A:** How many packs of 2 do you need for 6 shirts? Calculate the total cost.
3. **Shop B:** First, calculate the discounted price of a single shirt (25% off £12.40). Then, calculate the cost for 6 shirts.
4. **Shop C:** How many packs of 3 do you need for 6 shirts? Apply the "buy one, get one half price" offer to find the total cost.
5. Compare the three total costs and state which shop is the cheapest.
Full Answer
**Shop A:**
To get 6 shirts, we need 6 / 2 = 3 packs.
Cost = 3 × £19.00 = £57.00
**Shop B:**
The price of one shirt is reduced by 25%.
Discount = 25% of £12.40 = 0.25 × 12.40 = £3.10.
New price per shirt = £12.40 - £3.10 = £9.30.
(Alternatively, new price = 0.75 × £12.40 = £9.30)
Cost for 6 shirts = 6 × £9.30 = £55.80
**Shop C:**
To get 6 shirts, we need 2 packs of 3.
The offer is "Buy one pack, get another pack half price".
Cost = Price of first pack + Price of second pack (at half price)
Cost = £37.40 + (£37.40 / 2)
Cost = £37.40 + £18.70 = £56.10
**Conclusion:**
Comparing the costs:
Shop A: £57.00
Shop B: £55.80
Shop C: £56.10
The cheapest shop is Shop B.
This is a "best buy" problem. We need to calculate the cost of buying 6 shirts from each of the three shops and then compare them.
**Shop A:**
The shirts are sold in packs of 2. To get 6 shirts, you need 6 ÷ 2 = 3 packs.
Total cost = 3 × £19.00 = £57.00.
**Shop B:**
The shirts are sold individually. The price is £12.40 with a 25% discount.
A 25% discount means you pay 100% - 25% = 75% of the original price.
Price per shirt = 0.75 × £12.40 = £9.30.
Total cost for 6 shirts = 6 × £9.30 = £55.80.
**Shop C:**
The shirts are sold in packs of 3. To get 6 shirts, you need 6 ÷ 3 = 2 packs.
The offer is "buy one pack, get another pack half price".
Cost of the first pack = £37.40.
Cost of the second pack = £37.40 ÷ 2 = £18.70.
Total cost = £37.40 + £18.70 = £56.10.
**Comparison:**
- Shop A: £57.00
- Shop B: £55.80
- Shop C: £56.10
The lowest cost is £55.80, which is at Shop B.
Common mistakes
✗ For Shop B, calculating the discount (£3.10) but forgetting to subtract it from the original price.
✗ For Shop C, calculating the price of one pack and multiplying by 2, ignoring the offer.
✗ For Shop C, halving the price of both packs.
✗ Making arithmetic errors in multiplication or addition.
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