Ratio, proportion and rates of change · KS3

Money and Best Buys

Which bottle is the better deal? Don't guess — work out the price for one unit (one gram, one ml, one item) and compare. The smaller unit price wins. This question is on almost every Foundation paper.

National curriculum KS3: solve problems involving direct proportion; use compound units such as unit pricing; financial mathematics

1 · Unit price: the fair test

Price ÷ amount = price for one unit. For groceries, "price per 100 g" is often easiest: divide the price by the number of grams, then multiply by 100.

2 · Best buy: compare two offers

Work out the unit price of each offer. Cheaper per unit = better buy. Try changing the numbers — the bigger pack does not always win.

Offer A
Offer B

Exam tip: show the division. Marks come from the working "180 ÷ 250 = 0.72p per g" (or per 100 g), not just from naming the winner. Compare both offers in the same unit.

3 · Special offers as multipliers

Shops dress discounts up in different clothes. Turn each offer into "what you pay for what you get" and they become easy to compare.

4 · Have I got enough? Change and budgets

Add up the costs, compare with what you have, and give the change. Keep everything in the same unit (all pounds, or all pence) before adding.

Worked examples

400 g for £3.00 or 650 g for £4.55 — which is the better buy?
Offer 1 per 100 g: 300p ÷ 4 = 75p.
Offer 2 per 100 g: 455p ÷ 6.5 = 70p.
Answer: the 650 g pack — 70p per 100 g is cheaper.
"3 for 2" on £1.20 chocolate bars
You get 3 bars, you pay for 2: £2.40.
Per bar: £2.40 ÷ 3 = 80p, instead of £1.20.
Bus £2.15, meal £4.60, drink 85p. Paying with £10 — change?
Same units first: 85p = £0.85.
Total: 2.15 + 4.60 + 0.85 = £7.60.
Change: 10 − 7.60 = £2.40.

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