Best Buy Problems –

Best buy problems are one of the most practical topics in GCSE Maths — they test your ability to compare prices and quantities to determine which deal offers better value. The key technique is finding the unit price or the price per common quantity.

What Are Best Buy Problems?

A best buy problem gives you two or more products (or pack sizes) at different prices and asks you to work out which is better value for money. The standard approach is to calculate the cost per single item, per gram, per litre, or per any common unit so that a fair comparison can be made.

There are two equivalent methods: you can find the price per unit (divide price by quantity) or the quantity per pound/penny (divide quantity by price). Either method will give the correct answer, but you must use the same method for all options to make a fair comparison.

In real-world contexts, best buy questions may involve special offers such as "buy 2 get 1 free" or "20% off," which you need to account for before comparing.

These questions test proportional reasoning in a practical context and almost always require you to show your working clearly.

Key Formulas

Step-by-Step Method

1. For each option, identify the total cost and the total quantity.
2. If there is a special offer, adjust the effective quantity or price accordingly.
3. Calculate the unit price for each option (cost ÷ quantity) using the same unit.
4. The option with the lowest unit price is the best buy.

Worked Example 1 — Foundation Level

Question: A 500 g box of cereal costs £2.40. A 750 g box of the same cereal costs £3.30. Which is better value?

Working: 500 g box: £2.40 ÷ 500 = 0.48p per gram 750 g box: £3.30 ÷ 750 = 0.44p per gram 0.44p < 0.48p

Answer: The 750 g box is better value.

Worked Example 2 — Higher Level

Question: Shop A sells 4 batteries for £3.60. Shop B sells 6 batteries for £5.10. Shop B also has a "buy 6 get 2 free" offer. Which shop offers the best value?

Working: Shop A: £3.60 ÷ 4 = £0.90 per battery Shop B (with offer): You pay for 6 but get 8 batteries. £5.10 ÷ 8 = £0.6375 per battery £0.6375 < £0.90

Answer: Shop B is better value.

Worked Example 3 — Exam Style

Question: A 2-litre bottle of juice costs £1.80. A pack of 6 × 330 ml cartons of the same juice costs £2.70. Which is better value? You must show your working.

Working: Bottle: £1.80 ÷ 2000 ml = 0.09p per ml Pack: total volume = 6 × 330 = 1980 ml. £2.70 ÷ 1980 = 0.1364p per ml (4 d.p.) 0.09p < 0.1364p

Answer: The 2-litre bottle is better value.

Common Mistakes

• Comparing different units. You must compare like with like — both in pence per gram, or both in pence per ml, etc. Do not compare pence per gram with pounds per kg without converting.
• Forgetting special offers. If one option has a "3 for 2" deal, adjust the quantity to include the free items before calculating the unit price.
• Rounding too early. Keep several decimal places during the comparison and only round at the very end, otherwise you may conclude the wrong option is cheaper.
• Not showing working. Best buy questions always require a comparison calculation. Just stating the answer without working earns no marks.

Exam Tips

• Always show the unit price calculation for each option — this is where the method marks are.
• Clearly state which option is better value and why (lower cost per unit).
• If the question says "you must show your working," you will get no marks for a correct answer without it.
• Converting everything to pence avoids decimal confusion with pounds.

Practice Questions

Q1 (Foundation): A 400 g tin of beans costs 52p. A 250 g tin costs 35p. Which is better value?

Q2 (Foundation): 5 pens cost £2.25. 8 pens cost £3.44. Which is the better buy?

Q3 (Higher): A shop sells 500 ml of shampoo for £3.50. It also sells 200 ml for £1.60 with a "buy 2 get 1 free" offer. Which is better value?

Practise best buy problems with instant feedback — completely free on GCSEMathsAI.

Related Topics

• Ratio Basics and Sharing
• Unit Conversions
• Percentages

Summary

• Best buy problems compare value for money across different pack sizes or offers.
• Calculate the unit price (cost per gram, per ml, per item) for each option.
• The option with the lowest unit price is the best buy.
• Account for special offers by adjusting the effective quantity before dividing.
• Always show full working and clearly state your conclusion.
• You can also compare by finding how much you get per penny — the option giving the most per penny is the best buy.
• Keep several decimal places during comparison and only round at the end.