GCSE Maths Practice: best-value

Question 9 of 10

Pen packs come in different sizes and prices. Compare the cost per pen to find the best value.

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\( \begin{array}{l} \text{Which pen packs give the best value for money?} \end{array} \)

Select all correct options:

Always divide the total cost by the number of items.

Best Value with Individual Items

Best value questions do not always involve weights or volumes. Very often, GCSE Maths uses everyday situations where items are sold in packs containing different numbers of the same product. Examples include pens, pencils, notebooks, batteries, or drinks cans. In these cases, the goal is to find which pack gives the lowest cost for one item.

Looking only at the total price can be misleading. A larger pack may cost more overall but still be cheaper per item. Similarly, a smaller pack may look cheaper but actually cost more for each item.

The Cost Per Item Method

To solve best value problems involving individual items, calculate the cost per item.

  1. Identify how many items are in each pack.
  2. Divide the total price by the number of items.
  3. Compare the cost per item.

The pack with the lowest cost per item offers the best value for money.

Worked Example

A shop sells packs of notebooks:

  • 5 notebooks for £2.25
  • 8 notebooks for £3.60
  • 10 notebooks for £4.50

Calculate the cost per notebook:

  • £2.25 ÷ 5 = £0.45 per notebook
  • £3.60 ÷ 8 = £0.45 per notebook
  • £4.50 ÷ 10 = £0.45 per notebook

All packs have the same unit cost, so they offer equal value.

Another Example

Batteries are sold as:

  • 4 batteries for £1.40
  • 6 batteries for £2.10
  • 3 batteries for £1.05

Dividing the price by the number of batteries allows a fair comparison of value.

Common Mistakes

  • Comparing prices only: The cheapest pack overall is not always the best value.
  • Forgetting unit cost: Always calculate cost per item.
  • Assuming only one answer: Sometimes more than one pack can have the same unit price.

Real-Life Applications

Cost-per-item calculations are used frequently when shopping for stationery, household goods, or bulk items. Supermarkets often encourage customers to buy larger packs, but knowing how to calculate unit cost helps you decide whether the offer is genuinely good.

This skill is especially useful for budgeting and avoiding misleading deals.

Frequently Asked Questions

Can more than one pack be best value?
Yes. If two packs have the same cost per item, they offer equal value.

What if the numbers are awkward?
Use a calculator or work carefully with decimals.

Is this common in GCSE exams?
Yes. Best value questions using item counts appear regularly on Foundation papers.

Study Tip

Whenever items are sold in packs, divide the price by the number of items before choosing an answer.

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