GCSE Maths Practice: best-value

Higher GCSE Best Value with Discrete Items and Tie-Breaking

At Higher tier GCSE Maths, best value questions sometimes include an extra layer of reasoning. It is not always enough to find the lowest cost per item — you may also need to compare options that have the same unit price. In these cases, examiners expect you to consider which option offers better overall value.

In this question, toilet paper is sold in packs containing different numbers of rolls. Two of the packs have the same cost per roll, while the third is more expensive per roll. This means the decision cannot be made purely by unit price alone.

The Core Method: Cost per Item

For products sold as individual items, the fairest comparison is the cost per item.

1. Divide the total price by the number of items.
2. Compare the unit costs.
3. If unit costs are equal, compare the pack sizes.

When two packs cost the same per item, the larger pack is usually considered better value because you receive more items for the same unit cost.

Worked Example

A shop sells kitchen roll as:

• 4 rolls for £1.60
• 8 rolls for £3.20
• 12 rolls for £5.10

First, calculate the cost per roll:

• £1.60 ÷ 4 = £0.40 per roll
• £3.20 ÷ 8 = £0.40 per roll
• £5.10 ÷ 12 ≈ £0.43 per roll

The first two packs have the same unit price, but the 8-roll pack offers more rolls at that price, making it the better value option.

Another Higher-Tier Example

Paper towels are sold as:

• 6 rolls for £2.70
• 10 rolls for £4.50
• 15 rolls for £7.20

Two packs may work out to the same cost per roll, so comparing pack size becomes the deciding factor.

Common Higher-Tier Mistakes

• Stopping at unit price: When unit prices match, more reasoning is needed.
• Choosing the cheapest total price: Cheapest overall is not always best value.
• Ignoring pack size: Larger packs can offer better value when unit cost is equal.

Real-Life Applications

Supermarkets often price household goods like toilet paper, kitchen roll, and tissues so that medium-sized packs offer the best balance of value and affordability. Shelf labels may show unit prices, but shoppers still need to decide which pack suits them best.

Understanding how to compare discrete items helps you avoid overpaying for everyday essentials.

Frequently Asked Questions

What if two packs have exactly the same unit price?
The larger pack is generally considered better value.

Is this logic used in GCSE exams?
Yes. Higher-tier questions often include a tie-breaker situation.

Should I ever choose the smaller pack?
Only if the question asks about convenience rather than value.

Exam Tip

If unit prices are equal, compare the quantities — more items for the same unit cost means better value.