Problem 5 · 2022 Math Kangaroo
Easy
Algebra & Patterns
substitutionsum-constraint
Anna, Beatrice and Clara are 15 years old altogether. Anna and Beatrice together are 11 years old, and Beatrice and Clara together are 12 years old. How old is the oldest of the three?
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Answer: E — 8
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Hint 1 of 2
You know all three together, and two of the pairs. Subtract a pair total from the full total.
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Hint 2 of 2
The total minus a pair gives the third person's age; do this to find each age.
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Approach: subtract pair sums from the grand total
- All three add to 15. Anna+Beatrice = 11, so Clara = 15-11 = 4.
- Beatrice+Clara = 12, so Anna = 15-12 = 3, and Beatrice = 15-3-4 = 8.
- The oldest is Beatrice at 8, so the answer is E.
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