Problem 9 · 2025 Math Kangaroo
Medium
Algebra & Patterns
ratiosubstitution
Katrin and Thomas are both celebrating their birthday today. Thomas notices that \(\frac{1}{19}\) of Katrin's age is the same as \(\frac{1}{17}\) of his. Together they are older than 40 years and younger than 100 years. How old is Katrin?
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Answer: C — 38
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Hint 1 of 2
If Katrin/19 equals Thomas/17, both ages are multiples of the same number.
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Hint 2 of 2
Write K=19k, T=17k and use 40 < K+T < 100.
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Approach: common-multiple substitution
- From K/19 = T/17, set K = 19k and T = 17k.
- Total K+T = 36k must satisfy 40 < 36k < 100, so k = 2.
- Katrin = 19×2 = 38.
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