GCSE Maths Practice: best-value

Question 2 of 10

Smoothies are sold in different bottle sizes. Compare their unit prices carefully.

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\( \begin{array}{l} \text{Smoothie offers:} \\ \text{A: 300 ml for £1.35} \\ \text{B: 500 ml for £2.00} \\ \text{C: 1 L for £4.20} \\ \text{Which option gives the best value?} \end{array} \)

Choose one option:

Scaled units like 100 ml often make Higher-tier comparisons clearer.

Higher GCSE Best Value Using Price per 100 ml

At Higher tier GCSE Maths, best value questions often go beyond simple cost per litre. Instead, you may be asked to compare prices using a scaled unit such as price per 100 ml. This tests whether you understand that the choice of unit is flexible, as long as it is applied consistently.

In this question, smoothie bottles are sold in three very different sizes. Although one option may look cheaper or larger at first glance, visual judgement alone is unreliable. The purpose of using a unit like 100 ml is to make a fair comparison while keeping the arithmetic manageable.

Why Use 100 ml as the Unit?

Using price per 100 ml is especially useful when:

  • Volumes are not neat multiples of a litre
  • Products are relatively small
  • You want to avoid awkward decimal division by litres

As long as the same unit is used for every option, the comparison remains fair.

Step-by-Step Method

  1. Write each volume in millilitres.
  2. Divide each volume by 100 to find the number of 100 ml units.
  3. Divide the price by the number of units.
  4. Compare the resulting unit prices.

The option with the lowest price per 100 ml gives the best value.

Worked Example

A café sells fruit juice in the following bottles:

  • 250 ml for £1.10
  • 400 ml for £1.68
  • 800 ml for £3.36

First, find the number of 100 ml units:

  • 250 ml = 2.5 units
  • 400 ml = 4 units
  • 800 ml = 8 units

Now divide the price by the units:

  • £1.10 ÷ 2.5 = £0.44 per 100 ml
  • £1.68 ÷ 4 = £0.42 per 100 ml
  • £3.36 ÷ 8 = £0.42 per 100 ml

This shows how different-sized bottles can sometimes offer the same value.

Another Higher-Tier Example

Protein shakes are sold as:

  • 330 ml for £1.65
  • 500 ml for £2.40
  • 1 litre for £4.60

Using price per 100 ml allows all options to be compared fairly, even though one is given in litres.

Common Higher-Tier Mistakes

  • Using mixed units: All prices must be compared using the same unit.
  • Rounding too early: Rounding during calculations can change which option appears cheapest.
  • Assuming larger bottles are better value: Bigger does not always mean cheaper per unit.

Real-Life Applications

Price-per-100-ml comparisons are widely used on supermarket shelf labels for drinks, sauces, shampoos, and toiletries. This helps customers compare products quickly even when sizes vary.

Being confident with this method helps you avoid misleading offers and make informed purchasing decisions.

Frequently Asked Questions

Can I always choose 100 ml?
Yes, as long as it is sensible and used consistently.

Why not always use cost per litre?
For smaller products, 100 ml often gives clearer numbers.

Is this method expected at Higher tier?
Yes. GCSE Higher exams regularly include scaled-unit best value questions.

Exam Tip

Choose a unit that simplifies the arithmetic, but never mix units during the comparison.

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