Problem 9 · 2014 Math Kangaroo
Medium
Fractions, Decimals & Percents
work-backwarddivision
A bowl was full of sweets. Raphael took half of them out. Afterwards Emanuel took out half of the remaining sweets. Now there are only 12 sweets left in the bowl. How many sweets were in the bowl to begin with?
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Answer: E — 48
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Hint 1 of 3
Start at the end with the 12 sweets that are left and walk backwards.
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Hint 2 of 3
Each boy took half, so the 12 left is half of what was there just before him.
Still stuck? Show hint 3 →
Hint 3 of 3
Going back one step means doubling, so double, then double again.
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Approach: walk backwards, doubling at each step
- The 12 left over is half of what was in the bowl before Emanuel reached in, so before Emanuel there were 12 + 12 = 24.
- Those 24 are half of what was there before Raphael, so the bowl started with 24 + 24 = 48.
- Answer: 48.
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