Problem 13 · 2019 Math Kangaroo
Medium
Algebra & Patterns
work-backward
In a witch’s garden there are 30 animals: dogs, cats and mice. The witch changes 6 dogs into 6 cats and then 5 cats into 5 mice. Now there is an equal number of dogs, cats and mice. How many cats were there to start with?
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Answer: C — 9
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Hint 1 of 3
At the end the three kinds are equal, and 30 splits into three equal piles.
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Hint 2 of 3
Follow only the cats: first they go up, then they go down.
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Hint 3 of 3
Work the cat count backwards from its final value to its start.
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Approach: work backward from 10 cats
- At the end the three kinds are equal, so each is 30 ÷ 3 = 10; in particular there are 10 cats at the end.
- Cats gained 6 (the dogs that became cats) and then lost 5 (the cats that became mice), a net change of 6 − 5 = +1.
- So the cats started 1 fewer than they ended: 10 − 1 = 9 cats (C).
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