Problem 7 · 2023 Math Kangaroo
Medium
Logic & Word Problems
ages
If one adds the ages of all members of a family of five together, one gets 80. The two youngest children are 6 and 8 years old. What was the sum of the ages of the family members 7 years ago?
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Answer: D — 46
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Hint 1 of 2
Seven years ago, was the youngest child even born yet?
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Hint 2 of 2
Only count the people who existed seven years ago, and subtract 7 from each of their current ages.
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Approach: work backward in time, counting who was alive
- Now the five ages total 80; the youngest two are 6 and 8.
- Seven years ago the 6-year-old was not yet born, so only 4 people existed.
- Remove the 6-year-old: the other four total 80 − 6 = 74 now.
- Seven years ago those four were each 7 younger: 74 − 4·7 = 46.
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