Problem 4 · 2015 Math Kangaroo
Easy
Ratios, Rates & Proportions
ratioproportion
Anna, Beate and Cindy buy a bag of 30 biscuits together. They get 10 biscuits each. But Anna has paid 80 cents, Beate 50 cents and Cindy 20 cents. How many more biscuits should Anna have got, if they had shared them in proportion with the amount they had each paid?
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Answer: E — 6
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Hint 1 of 2
Split the 30 biscuits in the same ratio as the money paid: 80 : 50 : 20.
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Hint 2 of 2
Simplify 80 : 50 : 20 to 8 : 5 : 2 and find Anna's fair share, then subtract the 10 she got.
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Approach: share in proportion to money paid
- The payments 80 : 50 : 20 simplify to 8 : 5 : 2, which is 15 equal parts.
- 30 biscuits over 15 parts means 2 biscuits per part.
- Anna's fair share = 8 × 2 = 16 biscuits.
- She already received 10, so she should have got 16 − 10 = 6 more.
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