Problem 22 · 2018 Math Kangaroo
Stretch
Algebra & Patterns
substitution
The sum of Kathi's age and her mother's age is 36. The sum of her mother's age and her grandmother's age is 81. How old was Kathi's grandmother when Kathi was born?
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Answer: C — 45
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Hint 1 of 2
Subtract the two given sums to compare the grandmother's age with Kathi's directly.
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Hint 2 of 2
The gap between grandmother and Kathi is exactly her age when Kathi was born.
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Approach: subtract the two equations to get the age gap
- Kathi + mother = 36 and mother + grandmother = 81.
- Subtracting, grandmother - Kathi = 81 - 36 = 45.
- When Kathi was born her age was 0, so the grandmother was 45.
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