Best buy problems GCSE maths questions ask you to compare two or more differently sized packs and decide which offers better value for money. The reliable method is unit pricing: work out the cost (or amount) per single unit for each option, then compare those unit values directly, since comparing total prices alone is misleading.
What is a best buy problem?
A best buy problem presents two or more products in different pack sizes, usually with different total prices, and asks which represents the best value for money. These questions sit within the ratio and proportion topic at GCSE, because comparing value fairly means comparing a proportional rate — price per gram, price per litre, or price per item — rather than comparing raw totals.
Exam questions typically give quantities in grams, millilitres, or item counts, alongside prices in pounds and pence, and expect a clearly stated conclusion supported by working.
How do you find the unit price?
- Identify the price and the quantity for each option.
- Divide the price by the quantity to find the cost per single unit (per gram, per millilitre, or per item).
- Compare the unit prices directly — the smaller unit price is the better value.
Worked example: A 400g box of cereal costs £2.20. A 600g box of the same cereal costs £3.00. Which is better value?
Unit price of the 400g box: $2.20 \div 400 = £0.0055$ per gram.
Unit price of the 600g box: $3.00 \div 600 = £0.0050$ per gram.
The 600g box costs less per gram, so it is the better value.
How do you compare unit prices when the numbers are awkward?
Unit prices in pounds per gram are often tiny decimals that are hard to compare at a glance. A common exam technique is to scale up to a more convenient unit, such as price per 100g, so the numbers are easier to read and compare.
Worked example: Compare the same cereal boxes using price per 100g instead.
400g box: $\frac{2.20}{400} \times 100 = £0.55$ per 100g.
600g box: $\frac{3.00}{600} \times 100 = £0.50$ per 100g.
The conclusion matches the earlier answer — the 600g box is cheaper per 100g, confirming it is the better value — but the numbers are easier to compare directly at a glance.
What if you need to compare quantity per pound instead of price per unit?
Some questions ask the reverse: how much product you get for your money, rather than how much each unit costs. This uses the same idea, but with quantity divided by price instead of price divided by quantity.
Worked example: A 250ml bottle of juice costs £1.25. A 750ml bottle costs £3.50. Which gives more juice per pound spent?
250ml bottle: $250 \div 1.25 = 200$ ml per £1.
750ml bottle: $750 \div 3.50 = 214.3$ ml per £1 (to 1 decimal place).
The 750ml bottle gives more juice per pound spent, so it is the better value — the same conclusion you would reach comparing price per ml, just approached from the opposite direction.
What is the step-by-step method for any best buy question?
- Write down the price and quantity for each option clearly.
- Choose a consistent unit to compare — per gram, per 100g, per litre, or per item, whichever suits the numbers.
- Divide to find each option's rate in that chosen unit.
- Compare the rates directly, remembering that a lower cost-per-unit or a higher quantity-per-pound both indicate better value.
- State your conclusion clearly, naming the better-value option and showing the figures that support it.
Always finish with a sentence conclusion in exam answers — GCSE mark schemes often award a mark specifically for stating which option is better value, separate from the marks for correct calculation.
How do multipack and special offer questions differ?
Some best buy questions involve a "3 for 2" or "buy one get one half price" offer instead of two differently sized packs. The method is the same in principle: find the effective total price paid for the total quantity received, then convert that into a unit price for comparison.
Worked example: A shop sells cans of drink at £0.80 each, or in a "3 for £2" multipack. Which is better value?
Buying individually: £0.80 per can.
Multipack: $2.00 \div 3 = £0.667$ per can (to 3 decimal places).
The multipack works out cheaper per can, at roughly 67p compared to 80p buying individually, so the multipack is the better value.
What table layout helps compare more than two options?
| Product | Price | Quantity | Price per 100g |
|---|---|---|---|
| Brand A | £1.80 | 300g | £0.60 |
| Brand B | £2.40 | 450g | £0.53 |
| Brand C | £3.50 | 700g | £0.50 |
Setting out three or more options in a table like this makes the comparison immediate — Brand C has the lowest price per 100g, so it represents the best value of the three, even though it has the highest total price.
Frequently asked questions
Why can't you just compare the total prices?
Comparing total prices alone ignores the fact that the pack sizes are different. A £3.00 pack might look more expensive than a £2.20 pack, but if it contains proportionally much more product, it could actually be the cheaper option per unit — which is exactly why unit pricing is the correct method.
What unit should I use for price per unit?
Choose whatever unit makes the numbers easiest to compare, such as price per gram, per 100g, per litre, or per item. There is no single "correct" unit as long as you apply the same unit consistently to every option being compared in the question.
Do I always divide price by quantity?
Usually yes, to find the cost per unit, where a lower value means better value. If a question instead asks for the quantity received per pound spent, divide quantity by price instead, where a higher value then means better value — read the question carefully to see which direction is being asked for.
How do multipacks and special offers fit into best buy questions?
Treat the multipack as a single option with its own total price and total quantity, then convert to the same unit price used for the other options. Once every option is expressed as a price per unit, offers and multipacks compare exactly the same way as any standard best buy problem.
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