GCSE Maths Practice: best-value

Question 3 of 10

Smoothies are sold in different bottle sizes. Use price per 100 ml to compare their value.

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

Choose one option:

Using price per 100 ml often makes Higher-tier comparisons easier.

Higher GCSE Best Value Using Scaled Units

At Higher tier GCSE Maths, best value questions often require more than simply finding cost per litre. Instead, you may be asked to compare prices using a scaled unit such as per 100 ml. This adds an extra layer of difficulty, as it tests whether you can choose and apply a sensible comparison unit.

In this question, smoothie bottles are sold in very different sizes, ranging from a small bottle to a large 1 litre bottle. Comparing total prices alone would be misleading, as the largest bottle costs the most overall but may not be the best value.

Why Use Price per 100 ml?

Using price per 100 ml is helpful when:

  • Volumes are awkward decimals
  • Products are smaller than 1 litre
  • You want to avoid dividing by large numbers

This method keeps numbers manageable while still allowing a fair comparison.

Step-by-Step Method

  1. Convert all volumes to millilitres if necessary.
  2. Divide each volume by 100 to find how many 100 ml units there are.
  3. Divide the price by the number of 100 ml units.
  4. Compare the unit prices.

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

Worked Example

A café sells iced coffee in the following sizes:

  • 250 ml for £1.20
  • 400 ml for £1.80
  • 750 ml for £3.30

First, work out the number of 100 ml units:

  • 250 ml = 2.5 units
  • 400 ml = 4 units
  • 750 ml = 7.5 units

Now divide price by units:

  • £1.20 ÷ 2.5 = £0.48 per 100 ml
  • £1.80 ÷ 4 = £0.45 per 100 ml
  • £3.30 ÷ 7.5 = £0.44 per 100 ml

Comparing these values shows which drink offers the lowest cost per 100 ml.

Another Higher-Tier Example

Energy drinks are sold as:

  • 330 ml for £1.65
  • 500 ml for £2.40
  • 1 litre for £5.00

Using price per 100 ml helps compare all options fairly without needing to convert everything to litres.

Common Higher-Tier Mistakes

  • Using different units: All options must use the same unit (per 100 ml).
  • Rounding too early: Keep decimals until the final comparison.
  • Assuming bigger is better: Larger bottles can still be worse value.

Real-Life Applications

Price-per-100-ml comparisons are widely used in supermarkets, cafés, and convenience stores. Shelf labels often show cost per 100 ml for drinks, sauces, and toiletries. This allows customers to compare products quickly even when bottle sizes vary.

Understanding this skill helps you recognise genuinely good deals and avoid being misled by larger packaging.

Frequently Asked Questions

Why not always use cost per litre?
For smaller volumes, cost per 100 ml produces clearer and more manageable numbers.

Can I choose my own unit?
Yes, as long as it is sensible and used consistently.

Is this common in Higher exams?
Yes. GCSE Higher papers often include best value questions using scaled units.

Exam Tip

Always choose a unit that makes the arithmetic easier, but keep it consistent across all options.

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