Kevin bought tarts and buns for a family gathering. He bought 47 as many buns as tarts. Each bun cost 35 as much as each tart. Each bun cost $4.50. He paid $345 more on the tarts than on the buns.
- How much did he pay for each tart?
- How many tarts did he buy?
Need a hint?
Find the tart price first from the bun price using the fraction 35, then compare 7 tarts with 4 buns.
Worked answer
- (a) Bun price is 35 of tart price, so $4.50 is 3 equal parts.
- (a) One part = $4.50 ÷ 3 = $1.50, so the tart = 5 parts = $7.50.
- (b) Take 7 tarts and 4 buns as one set: tarts cost 7 × $7.50 = $52.50.
- (b) Buns in that set cost 4 × $4.50 = $18, so the difference per set = $52.50 − $18 = $34.50.
- (b) Number of sets = $345 ÷ $34.50 = 10, so tarts = 7 × 10 = 70.
The mistake this question tests
Stopped at one part in ratio
Multiplying $4.50 by 35 gives the tart price as $2.70, which reverses the relationship; the bun is the cheaper item, so the tart must be bigger than $4.50.
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