AQA · Mathematics · 8300
GCSE Maths: Money: Greatest/Maximum
Ratio & Proportion · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Money: Greatest/Maximum (Corbettmaths Video 400), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.
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How do you find the greatest number of items you can buy with a fixed amount of money?
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Divide the money by the price of one item and round DOWN to the nearest whole number.
Why is the answer to a 'greatest number' money problem always rounded down?
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You can only buy whole items, and rounding up would cost more than the money available.
Pencils cost 40p each. What is the greatest number you can buy with £3?
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7 pencils (300p ÷ 40p = 7.5, rounded down).
Rulers cost 80p each. How much change is left from £5 after buying as many as possible?
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20p (6 rulers cost £4.80; £5 − £4.80 = 20p).
How do you calculate the money left after buying the greatest number of items?
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Multiply the number bought by the unit price, then subtract this from the starting amount.
Chairs cost £24.79 each. What is the greatest number that can be bought with £1600?
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64 chairs (1600 ÷ 24.79 ≈ 64.5, rounded down).
Orla buys 8 hairbands at £3 each and gets £1 change. How much did she start with?
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£25 (8 × £3 = £24, plus £1 change).
To find the starting amount when you know the number bought, the unit price and the change: multiply number by price, then ? the change.
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add
Why does halving a price not always exactly double the number of items you can buy?
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Because of rounding down: e.g. £10 buys 5 packets at £1.80 but 11 packets at 90p, not 10.
At £1 = $1.24, how many $50 notes can Lara get for up to £800?
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19 notes (£800 × 1.24 = $992; 992 ÷ 50 = 19.84, rounded down).
What is the first step in a 'greatest number' problem involving a foreign exchange rate?
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Convert the pounds into the foreign currency by multiplying by the exchange rate, then divide by the note value and round down.
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