Problem 6 · 2019 Math Kangaroo
Medium
Algebra & Patterns
work-backward
Five friends bake gingerbread and then meet up for a tasting. Each one gives one of his gingerbreads to each of the other four people. Then everyone eats all of the gingerbread they were given. After that the number of gingerbreads has halved. How many gingerbreads did the five friends have to start with?
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Answer: D — 40
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Hint 1 of 2
Work out how many gingerbreads are eaten in total.
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Hint 2 of 2
The amount eaten equals half the starting number.
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Approach: total eaten = half the start
- Each of the 5 friends hands one gingerbread to each of the other 4, so 5 × 4 = 20 gingerbreads are given away and eaten.
- After eating, the count has halved, so the 20 eaten are exactly half of the start.
- Therefore they began with 2 × 20 = 40 gingerbreads.
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