Problem 7 · 2019 Math Kangaroo
Medium
Algebra & Patterns
sum-constraintwork-backward
The individual masses (in kg) of three kangaroos are three different integers. Together they weigh 97 kg. What is the maximum weight the lightest of the three can have?
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Answer: C — 31
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Hint 1 of 2
To make the lightest as big as possible, keep the three weights as close together as you can.
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Hint 2 of 2
Try three near-equal integers summing to 97 and adjust.
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Approach: push the three values close together
- Let the weights be a < b < c with a + b + c = 97.
- The lightest is largest when the three are nearly equal: 31, 32, 34 = 97.
- So the lightest can be at most 31 kg.
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