Problem 11 · 2019 Math Kangaroo
Medium
Fractions, Decimals & Percents
area-fractionwork-backward
Mother halves the birthday cake. One half she then halves again. Of that she again halves one of the smaller pieces. Of these smaller pieces she once more halves one of them (see diagram). One of the two smallest pieces weighs 100 g. How much does the entire cake weigh?
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Answer: D — 1600 g
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Hint 1 of 2
Each halving makes a piece half as big; the smallest piece is a fraction of the whole cake.
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Hint 2 of 2
Halving four times gives a sixteenth, so the 100 g piece is 1/16 of the cake.
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Approach: track the fraction of the whole
- Halving the cake repeatedly gives pieces of 1/2, 1/4, 1/8, and finally 1/16.
- The smallest piece is 1/16 of the cake and weighs 100 g.
- So the whole cake weighs 16×100 = 1600 g (D).
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