Farah spent a total of $560 to buy some cups and bowls for a school fair. She spent $160 more on cups than on bowls.
- Find the amount of money she spent on cups. [2]
- She bought 3 times as many cups as bowls. Each bowl costs $2 more than each cup. Find the cost of one cup. [3]
Need a hint?
In (b), imagine each bowl cost the same as a cup. How much would the bowls cost then? Compare that with the real cost to find the number of bowls.
Worked answer
- (a) Take away the extra $160: $560 − $160 = $400. This is two equal amounts, one for cups and one for bowls.
- (a) Each equal amount is $400 ÷ 2 = $200. So she spent $200 on bowls.
- (a) Cups: $200 + $160 = $360.
- (b) Let the number of bowls be 1 unit. Then the number of cups is 3 units.
- (b) If a bowl cost the same as a cup, the bowls would cost 13 of the cups' cost: $360 ÷ 3 = $120.
- (b) The bowls really cost $200, so the extra is $200 − $120 = $80.
- (b) Each bowl costs $2 more, so the number of bowls is $80 ÷ $2 = 40.
- (b) Number of cups = 3 × 40 = 120.
- (b) Cost of one cup = $360 ÷ 120 = $3.
Answer: $3
The mistake this question tests
Habit
Stopped at one part in ratio
Many pupils halve $560 to get $280 for each in (a), forgetting that cups cost $160 more. In (b) they often divide $360 by the number of bowls instead of the number of cups.
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