Problem 6 · 2021 Math Kangaroo
Medium
Algebra & Patterns
total-then-divide
In a jazz band, Giuseppe plays the saxophone, Sergio plays the trumpet and Eliana sings. They are all the same age. There are 3 more members of the band, who are 19, 20 and 21 years old. The average age of the jazz band is 21. How old is Eliana?
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Answer: C — 22
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Hint 1 of 2
Average 21 over 6 members means the total of all ages is 6×21.
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Hint 2 of 2
Subtract the three known ages; the rest splits equally among the three same-age members.
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Approach: use the total then divide
- Six members average 21, so their ages total 6×21 = 126.
- The three known members are 19+20+21 = 60, leaving 66 for the other three.
- Those three are the same age, so each is 66÷3 = 22.
- Eliana is 22, choice (C).
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