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    PracticeAQA GCSEAQA GCSE Maths Higher Tier Paper 3 CalculatorQuestion 06
    Medium5 marksStructured
    Ratio Proportion and Rates of ChangeHigherRatio Proportion and Rates of ChangeBest BuyPercentages

    AQA GCSE · Question 06 · Ratio Proportion and Rates of Change

    Shop A Pack of 2 £19.00 Shop B Was £12.40 Now 25% off 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

    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.
    Question 05All questionsQuestion 07.1

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