Problem 1 · 2016 Math Kangaroo
Medium
Algebra & Patterns
substitutionsum-constraint
The sum of the ages of Tom and Johann is 23. The sum of the ages of Johann and Alex is 24, and the sum of the ages of Alex and Tom is 25. How old is the oldest of them?
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Answer: D — 13
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Hint 1 of 3
Add all three given pair-sums together.
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Hint 2 of 3
The grand total counts every person twice, so half of it is the sum of all three ages.
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Hint 3 of 3
Subtract a known pair from that whole-group total to isolate one person's age.
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Approach: add the equations to get the total, then back out each age
- Adding the three pair-sums: 23+24+25 = 72.
- Each person is counted twice, so Tom+Johann+Alex = 36.
- Alex = 36 - (Tom+Johann) = 36 - 23 = 13; similarly Tom = 12, Johann = 11.
- The oldest is 13.
Mark:
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