Problem 13 · 2023 Math Kangaroo
Hard
Algebra & Patterns
ratio
A rope with length 95 m is cut into three pieces so that each piece is half as long again as the respective previous piece. How long is the longest of the three pieces?
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Answer: C — 45 m
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Hint 1 of 2
“Half as long again” means each piece is 1.5 times the previous one.
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Hint 2 of 2
Write the three pieces as x, 1.5x, 2.25x and add them to 95.
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Approach: geometric pieces summing to the whole
- Let the pieces be x, 1.5x, and 2.25x.
- Their sum is 4.75x = 95, so x = 20.
- The longest piece is 2.25·20 = 45.
- So the longest is 45 m.
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