GCSE Maths Practice: best-value

Question 6 of 10

Shampoo bottles come in different sizes. Use unit price per 100 ml to compare their value.

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\( \begin{array}{l} \text{Which shampoo bottle gives the best price per 100 ml?} \end{array} \)

Choose one option:

Using price per 100 ml helps compare smaller bottles accurately.

Higher GCSE Best Value Using Price per 100 ml

At Higher tier GCSE Maths, best value questions are designed to test precision and careful reasoning rather than quick estimation. When products are sold in different-sized containers, comparing total prices alone is unreliable. Instead, you must calculate a unit price, often using a scaled unit such as price per 100 ml.

In this question, shampoo bottles are sold in three different volumes. The prices are close together, and two of the unit prices are very similar. This means that rounding too early or making assumptions based on bottle size can easily lead to the wrong conclusion.

Why Use Price per 100 ml?

Using price per 100 ml is especially helpful when:

  • The volumes are less than one litre
  • The numbers involve decimals
  • You want to avoid dividing by awkward fractions of a litre

As long as the same unit is used consistently for all options, the comparison remains fair.

Step-by-Step Method

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

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

Worked Example

A shop sells body wash in the following bottles:

  • 300 ml for £1.68
  • 450 ml for £2.43
  • 600 ml for £3.30

First, calculate the number of 100 ml units:

  • 300 ml = 3 units
  • 450 ml = 4.5 units
  • 600 ml = 6 units

Now divide the price by the number of units:

  • £1.68 ÷ 3 = £0.56 per 100 ml
  • £2.43 ÷ 4.5 = £0.54 per 100 ml
  • £3.30 ÷ 6 = £0.55 per 100 ml

Comparing these values shows which bottle has the lowest unit cost.

Another Higher-Tier Example

Conditioner is sold as:

  • 200 ml for £1.20
  • 500 ml for £3.05
  • 750 ml for £4.50

Using price per 100 ml allows you to compare all three options accurately without converting to litres.

Common Higher-Tier Mistakes

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

Real-Life Applications

Supermarkets frequently show price per 100 ml on shelf labels for toiletries such as shampoo, conditioner, shower gel, and lotion. These labels help shoppers compare products quickly when bottle sizes vary.

Being confident with unit pricing helps you avoid misleading packaging and choose products based on real value rather than appearance.

Frequently Asked Questions

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

What if two unit prices are the same?
If unit prices match exactly, the products offer equal value.

Is this type of question common at Higher tier?
Yes. GCSE Higher papers frequently include scaled-unit best value questions.

Exam Tip

Keep decimal values exact until the final comparison, and double-check your arithmetic before choosing an answer.

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