Sheet № 174 · Foundation + Higher · AQA · Edexcel · OCR
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.
§Key definitions
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?
Answer:
The 750 g box is better value.
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?
§Formulas to memorise
Unit price = total cost ÷ number of items (or total quantity)
Amount per penny = total quantity ÷ total cost in pence
Worked example
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
⚠ 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.