2021 JMC 10 Problems/Problem 6

Problem 6

The sum of the ages of a family equals $78.$ Fifteen years later, the sum of their ages is equal to $153.$ How many people are in this family?

$\textbf{(A) } 4 \qquad\textbf{(B) } 5 \qquad\textbf{(C) } 7 \qquad\textbf{(D) } 9 \qquad\textbf{(E) } 10$

Solution

Suppose there are $N$ people in the family. After fifteen years, each person's age is increased by $15,$ and the entire sum of the entire family's age is increase by $15N.$ We have $15N + 78 = 153 \implies N=5.$

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2021 JMC 10 Problems/Problem 6

Problem 6

Solution