Problem 4 · 2018 Math Kangaroo
Medium
Algebra & Patterns
The distance from the top of the cat sitting on the table to the top of the cat sleeping on the floor is 150 cm. The distance from the top of the cat sleeping on the table to the top of the cat sitting on the floor is 110 cm. How high is the table?
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Answer: C — 130 cm
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Hint 1 of 2
Add the two given distances and see what each cat contributes.
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Hint 2 of 2
Each measurement is one sitting-cat height plus the table minus one sleeping-cat height; adding them cancels the cats.
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Approach: add the two measurements so the cat heights cancel
- Let the table height be t, a sitting cat add s above its base and a sleeping cat add p.
- First distance: t + s − p = 150. Second distance: t + p − s = 110.
- Adding the two equations: 2t = 260, so t = 130 cm.
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