GCSE Maths Practice: best-value

Question 5 of 10

Different juice bottles have different volumes and prices. Use unit price to find the best value.

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\( \begin{array}{l} \text{Which juice bottle gives the best value for money?} \end{array} \)

Choose one option:

Always compare prices using cost per litre.

Best Value Problems Using Volume

Best value questions are very common in GCSE Maths because they reflect everyday decisions people make when shopping. Products such as drinks, cleaning liquids, fuel, and cooking oils are often sold in different volumes and prices. Simply choosing the cheapest item is not always the best decision, because a larger bottle may cost more overall but less per litre.

In questions involving liquids, the key idea is to compare all options using the same unit of volume. This ensures that the comparison is fair and accurate.

Using Cost Per Litre

The most reliable way to compare liquid products is to calculate the cost per litre. This means finding how much one litre of the product costs for each option.

  1. Convert all volumes to litres. For example, 750 ml becomes 0.75 L.
  2. Divide the price by the volume in litres.
  3. Compare the costs per litre.

The lowest cost per litre represents the best value.

Worked Example

A shop sells milk in three bottles:

  • 1 litre for £1.45
  • 2 litres for £2.70
  • 500 ml for £0.85

Convert millilitres to litres, then calculate cost per litre:

  • £1.45 ÷ 1 = £1.45 per litre
  • £2.70 ÷ 2 = £1.35 per litre
  • £0.85 ÷ 0.5 = £1.70 per litre

Comparing these values shows which option is the cheapest per litre.

Another Example

Cooking oil is sold as:

  • 750 ml for £2.40
  • 1.5 litres for £4.20
  • 3 litres for £8.70

After converting all volumes to litres, divide the price by the volume to find the unit cost.

Common Mistakes

  • Forgetting unit conversion: Always convert millilitres to litres before dividing.
  • Comparing prices only: The lowest price is not always the best value.
  • Dividing incorrectly: Always divide price by volume, not volume by price.

Real-Life Applications

Supermarkets regularly display cost per litre on shelf labels to help customers compare drinks and household liquids. This same method is used when comparing petrol prices, bottled water, cleaning products, and even paint.

Understanding unit pricing helps you make smarter financial decisions and avoid misleading offers.

Frequently Asked Questions

Why do we use cost per litre?
It allows all options to be compared fairly using the same volume.

What if one bottle is already in litres?
You can use its volume directly without converting.

Is this topic common in GCSE exams?
Yes. Best value by volume appears frequently in Foundation papers.

Study Tip

Whenever liquids are compared using different bottle sizes, always calculate the cost per litre before choosing an answer.

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