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maw [93]
2 years ago
15

The average age three people running for election is 42. A fourth person joins the race and the average drops to 40. What is the

fourth person's age?
Mathematics
1 answer:
bogdanovich [222]2 years ago
5 0

Let a_1,\ldots,a_4 denote the ages of the 4 candidates. Then

\dfrac{a_1+a_2+a_3+a_4}4=40

a_1+a_2+a_3+a_4=160

\dfrac{a_1+a_2+a_3}3+\dfrac{a_4}3=\dfrac{160}3

The average age of the first 3 candidates is 42, so

\dfrac{a_4}3=\dfrac{160}3-42

\implies\boxed{a_4=160-3\cdot42=34}

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