GCSE Maths Practice: best-value

Question 1 of 10

Three different orange juice packs are sold in a shop. Find which one gives the best value for money.

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\( \begin{array}{l} \text{Orange juice packs:} \\ \text{A = 1L for £1.20} \\ \text{B = 2L for £2.00} \\ \text{C = 1.5L for £1.80} \\ \text{Which pack is the best value?} \end{array} \)

Choose one option:

Always compare prices using the same unit, such as cost per litre.

Understanding Best Value Problems

Best value questions are a common topic in GCSE Maths and appear frequently in real-life situations such as shopping, budgeting, and comparing deals. The key idea behind these problems is that prices alone cannot be compared fairly unless the quantities are the same. A larger item may cost more overall but still be better value if it costs less per unit.

In this question, the products are orange juice packs with different sizes and prices. Because the quantities are measured in litres, the fairest way to compare them is to calculate the cost per litre. This creates a common unit, allowing a direct comparison.

Step-by-Step Method

  1. Identify the unit you are comparing (litres in this case).
  2. For each option, divide the total price by the number of litres.
  3. Compare the results.
  4. The option with the lowest cost per unit represents the best value.

This method works for all similar problems, whether you are comparing food, fuel, fabric, or mobile phone data.

Worked Example

A supermarket sells three bottles of milk:

  • 1 litre for £0.95
  • 2 litres for £1.80
  • 3 litres for £2.85

To compare fairly, calculate the cost per litre:

  • £0.95 ÷ 1 = £0.95 per litre
  • £1.80 ÷ 2 = £0.90 per litre
  • £2.85 ÷ 3 = £0.95 per litre

The bottle with the lowest cost per litre would be the best value option.

Common Mistakes to Avoid

  • Comparing total prices only: The cheapest item overall is not always the best value.
  • Forgetting the units: Always check that quantities are measured in the same unit before comparing.
  • Incorrect division: Make sure you divide price by quantity, not the other way around.

Real-Life Applications

Best value calculations are used every day. Supermarkets display price-per-unit labels on shelves to help customers compare products quickly. Fuel prices are often compared by cost per litre, and mobile phone contracts are compared by cost per gigabyte of data.

Understanding this skill helps you make informed financial decisions and avoid misleading deals.

Frequently Asked Questions

Do I always divide price by quantity?
Yes. When finding value, dividing the total cost by the amount gives the cost per unit.

What if quantities are in different units?
Convert them into the same unit first (for example, millilitres to litres).

Is this topic assessed in exams?
Yes. Best value problems commonly appear in GCSE Maths Foundation papers.

Study Tip

Whenever you see a comparison involving prices and sizes, pause and ask: What is the cost per unit? This single question will guide you to the correct method every time.

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