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GCSE Maths · Ratio, proportion and rates of change
Best buys GCSE Questions and Worked Answers
Compare prices for the same quantity and units. A lower unit price is better value, but whole-pack restrictions or a fixed shopping requirement can change the cheapest purchase.
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Start with the meaning
What you need to know about best buys
Two packs of identical pens sit on a shelf. One costs less, but it also contains fewer pens. To compare value fairly, imagine splitting each pack's price equally between its pens. Four pens for £2.80 cost 70p each; six for £3.90 cost 65p each. The second pack costs more altogether but provides each pen more cheaply. This price for one item is a unit price.
See the idea first
Make the comparison fair
Both prices must refer to one pen, one kilogram or another common amount. Comparing £ per kilogram with pence per gram without conversion gives incompatible numbers. State the common unit beside each result.
| Pack | Quantity | Price | Price per item |
|---|---|---|---|
| A | 4 | £2.80 | 70p |
| B | 6 | £3.90 | 65p |
From problem to method
Typical problems you need to be able to solve
These are the main kinds of question in this topic. Each card first states the problem, then explains how to solve it.
Compare pack sizes
What the problem asks: Which is better value: 400 g for £1.60 or 750 g for £2.70?
How to solve it: Per 100 g, the prices are 40p and 36p. The 750 g pack is better value.
Include an offer
What the problem asks: Identical £3 bottles are sold three for the price of two. Find price per bottle.
How to solve it: Three bottles cost £6 in the offer, so the effective price is £2 per bottle when buying a complete offer group.
Buy enough whole packs
What the problem asks: You need at least seven pens. Four-packs cost £2.80; six-packs cost £3.90. Find the cheapest combination.
How to solve it: Two four-packs cost £5.60 and provide eight. One of each costs £6.70; two six-packs cost £7.80. The lowest unit-price pack does not give the cheapest purchase here.
A reliable routine
Compare equivalent quantities
Use unit prices or a common multiple when goods are comparable. Dividing by quantity assigns the total cost to equal units, making different pack sizes comparable.
- Convert quantities and prices to compatible units.
- Apply discounts or free-item offers to the actual purchase.
- Divide cost by quantity, keeping enough precision for comparison.
- For a required amount, check whole-pack combinations and state the cheapest feasible purchase.
Check: These are simplified exam comparisons assuming equal quality and no waste unless stated. Real purchases may also depend on quality, storage and budget. Any exchange rate in a question is hypothetical, not a current quote.
Fully worked
Best buys GCSE worked examples
Each solution explains the clue, why the method fits and how to check the result.
Example 1
Unit prices
Question
Compare 5 notebooks for £4.25 with 8 identical notebooks for £6.40.
Eight-pack: 80p per notebook instead of 85p.
Example 2
Mass units
Question
Compare 600 g for £2.10 with 1 kg for £3.20.
Per kg,
The 1 kg pack costs £3.20/kg instead of £3.50/kg.
Example 3
Common quantity
Question
Compare 3 batteries for £2.40 with 4 for £3.40 using twelve batteries.
Four three-packs cost 4 × £2.40 = £9.60. Three four-packs cost 3 × £3.40 = £10.20. Three-packs save 60p per twelve batteries.
Example 4
Three for two
Question
A bottle costs £2.70 with a three-for-two offer. Another shop charges £1.90 each. Compare three bottles.
Offer price: 2 × £2.70 = £5.40. Other shop: 3 × £1.90 = £5.70. The offer saves 30p, or 10p per bottle.
Example 5
Extra free
Question
A 500 g pack costs £2.40 and has 25% extra free. Compare with 750 g for £3.
Extra amount: 0.25 × 500 = 125 g, so receive 625 g. Cost per kg: £2.40/0.625 = £3.84. Other pack: £3/0.75 = £4/kg. Extra-free pack is better value.
Example 6
Whole-pack requirement
Question
You need at least 10 identical items. Packs of 4 cost £3; packs of 6 cost £4.80. Find the cheapest purchase, allowing mixed packs.
Three four-packs cost £9. Two six-packs cost £9.60. One of each gives exactly 10 for £7.80. No single pack suffices, and any three packs cost at least £9. One of each is cheapest.
10 original questions · total 27 marks
Best buys GCSE exam-style questions
Try each question before opening its fully worked answer. The difficulty rises through the set.
Before you startAllow about 32 minutes · Show your working. Give exact answers unless a question asks you to round, and include units where needed. · answers start collapsed
Per item
Six apples cost £1.50. Find price per apple.
Show worked answer
25p per apple.
Compare
Compare 4 rolls for £1.80 with 6 for £2.40.
Show worked answer
45p each versus 40p each. Six-pack is better value.
Per 100 g
A 350 g pack costs £1.40. Find price per 100 g.
Show worked answer
40p per 100 g.
Mixed units
Compare 800 g for £2.80 with 1.5 kg for £4.80.
Show worked answer
1.5 kg pack is cheaper per kg.
Buy one get one free
One bottle costs £4.60, buy one get one free. Find the effective price each when buying two.
Show worked answer
Two cost £4.60.
£2.30 each.
Discount
A 2 kg bag costs £7 with 20% off. Find its discounted price per kg.
Show worked answer
£2.80/kg.
Extra quantity
A 400 g pack has 50% extra free and costs £1.80. Find price per kg.
Show worked answer
Receive 400 × 1.5 = 600 g = 0.6 kg.
£3/kg.
Equal value
Are 3 items for £2.10 and 5 for £3.50 equal value?
Show worked answer
Yes: 70p each.
Minimum spend
You need at least 5 items. A pack of 5 costs £4; a pack of 8 costs £5.60. Which single pack minimises spend?
Show worked answer
The five-pack costs less in total and meets the requirement. The eight-pack has lower unit cost, but that is a different question.
Currency comparison
A book costs £12 or €15. Given £1 = €1.20 and no fees, which is cheaper?
Show worked answer
Convert the pound price:
£12 is cheaper than €15 by €0.60.
Examiner-style feedback
Common best buys mistakes
First compare the same quantity.
Free items or low unit prices may require more spending than the task allows.
Nearly equal unit prices can be misordered after coarse rounding.
30-second recap
Choose, carry out, check
Translate the wording before you reach for a rule.
- Use equal units.
- Apply the offer.
- Compare unit costs.
- Check the actual requirement.
Quick answers
Best buys FAQ
Must I use the unitary method?
No. Scaling both offers to a common quantity is equally valid.
Does best value always mean lowest spend?
No. Best value usually compares cost per unit; minimum spend meets a stated need as cheaply as possible.
Content standards
Curriculum and rights review
R5/R11 best-buy and unit-pricing contexts across tiers, with explicit whole-pack constraints. Questions, suggested marks, solutions and diagrams are original practice material, not official past-paper questions.
Official specification references