GCSE Maths Practice: best-value

Question 4 of 10

Coffee tins are sold in different sizes. Use unit price to compare their value.

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\( \begin{array}{l} \text{Which coffee tin offers the best value per 100 g?} \end{array} \)

Choose one option:

Using cost per 100 g helps compare products with awkward weights.

Higher GCSE Best Value Using Cost per 100 g

At Higher tier GCSE Maths, best value questions often involve weights that are not neat multiples of a kilogram. Instead of using cost per kilogram, it is sometimes more sensible to compare prices using a smaller unit such as cost per 100 g. This allows clearer calculations and more accurate comparisons.

In this question, coffee tins are sold in different sizes with prices that increase rapidly as the tin gets larger. Many students assume that buying more automatically gives better value, but this is not always true. The purpose of this question is to test whether you can apply unit pricing correctly rather than relying on assumptions.

Why Use Cost per 100 g?

Using cost per 100 g is particularly useful when:

  • Weights are given in grams rather than kilograms
  • The numbers are awkward decimals
  • You want to avoid converting to kilograms

As long as every option is compared using the same unit, the comparison remains fair.

Step-by-Step Method

  1. Check that all weights are in grams.
  2. Divide each weight by 100 to find the number of 100 g units.
  3. Divide the price by the number of 100 g units.
  4. Compare the unit costs carefully.

The option with the lowest cost per 100 g offers the best value.

Worked Example

A shop sells cocoa powder in the following tins:

  • 250 g for £3.25
  • 400 g for £5.40
  • 750 g for £10.50

First, find the number of 100 g units:

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

Now divide price by units:

  • £3.25 ÷ 2.5 = £1.30 per 100 g
  • £5.40 ÷ 4 = £1.35 per 100 g
  • £10.50 ÷ 7.5 = £1.40 per 100 g

Comparing these values shows which tin offers the lowest unit price.

Another Higher-Tier Example

Tea leaves are sold as:

  • 180 g for £2.70
  • 300 g for £4.80
  • 600 g for £9.90

Using cost per 100 g allows you to compare all options accurately without converting to kilograms.

Common Higher-Tier Mistakes

  • Assuming larger packs are better value: Bigger packs can sometimes be more expensive per unit.
  • Mixing units: Always use the same unit (per 100 g) for every option.
  • Rounding too early: Keep decimals until the final comparison.

Real-Life Applications

Supermarkets often display prices per 100 g for products such as coffee, tea, spices, and cheese. This helps customers compare premium items where prices rise quickly with size. Understanding unit pricing allows you to spot when smaller packs may actually be better value.

This skill is especially useful when shopping for branded goods, specialty foods, or bulk items with steep price differences.

Frequently Asked Questions

Why not always use cost per kilogram?
For smaller products, cost per 100 g often produces clearer numbers.

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

Is this type of question common at Higher tier?
Yes. GCSE Higher exams frequently include best value questions using scaled weight units.

Exam Tip

If the weights are given in grams, choosing cost per 100 g usually makes the maths easier and reduces errors.

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