Problem 19 · 2010 Math Kangaroo
Hard
Logic & Word Problems
work-backwardsum-constraint
The picture shows a hanging mobile. The mobile weighs 112 grams in total. (The weight of the sticks and threads is not counted.) How much does the star weigh?
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Answer: B — 7 g
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Hint 1 of 2
Each balanced bar hangs from its middle, so its two sides must weigh the same.
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Hint 2 of 2
Start with the whole 112 g at the top and keep halving as you follow the bars down to the star.
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Approach: halve the weight at each balanced bar
- The top bar splits the 112 g into two equal sides: \(112 \div 2 = 56\) g on the right.
- Going down the right side, halve again to \(56 \div 2 = 28\) g, then \(28 \div 2 = 14\) g for the small bar holding the circle and the star.
- That last bar splits 14 g equally, so the star weighs \(14 \div 2 = 7\) g — the answer is B.
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