2007 AMC 10B Problems/Problem 12

Problem

Tom's age is $T$ years, which is also the sum of the ages of his three children. His age $N$ years ago was twice the sum of their ages then. What is $T/N?$

$\textbf{(A) } 2 \qquad\textbf{(B) } 3 \qquad\textbf{(C) } 4 \qquad\textbf{(D) } 5 \qquad\textbf{(E) } 6$

Solution

Tom's age $N$ years ago was $T-N$ . The ages of his three children $N$ years ago was $T-3N,$ since there are three people. If his age $N$ years ago was twice the sum of the children's ages then, $\begin{align*}T-N&=2(T-3N)\\ T-N&=2T-6N\\ T&=5N\\ T/N&=\boxed{\mathrm{(D) \ } 5}\end{align*}$

2007 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 11	Followed by Problem 13
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2007 AMC 10B Problems/Problem 12

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