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Ratio & Proportion · Foundation & Higher

Best buys & exchange rates

Best buy problems compare value for money by finding cost per unit or units per pound. Exchange rate problems convert between currencies using a given rate.

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Key facts to remember

  • 1To find the best buy: calculate the cost per gram (or unit) for each option.
  • 2Alternatively, find the amount per penny/pound — the higher amount is better value.
  • 3Exchange rate: Pounds → Euros: multiply by the rate. Euros → Pounds: divide by the rate.
  • 4Always compare quantities using the same unit.
  • 5Check the question — sometimes "best buy" means lowest cost per unit, sometimes most for money.
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Worked examples

Example 1

Pack A: 500 g for £2.20. Pack B: 750 g for £3.15. Which is better value?

Working

  1. Pack A: £2.20 ÷ 500 = 0.44p per gram
  2. Pack B: £3.15 ÷ 750 = 0.42p per gram
  3. Pack B is cheaper per gram → better value
AnswerPack B is better value (0.42p/g vs 0.44p/g)
Example 2

The exchange rate is £1 = €1.15. Convert £250 to euros and €460 to pounds.

Working

  1. £250 to euros: 250 × 1.15 = €287.50
  2. €460 to pounds: 460 ÷ 1.15 = £400
Answer£250 = €287.50; €460 = £400
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Common mistakes

✗Choosing the larger pack as better value without actually calculating the unit price.
✗Multiplying when converting foreign currency back to pounds (should divide).
✗Not comparing the same unit — one in pence per gram, another in pounds per kg.
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Exam tips

✓Always calculate the price per unit (per gram, per ml, etc.) for each option before comparing.
✓State which is better value and why — give numerical evidence.

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