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2007 AMC 10B Problem 12

Problem 12 of 25IntermediateAlgebra

Tom’s age is TT years, which is also the sum of the ages of his three children. His age NN years ago was twice the sum of their ages then. What is TN?\frac{T}{N}?

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Solution

NN years ago Tom’s age was T−N,T-N, and the sum of his three children’s ages was T−3N.T-3N. The condition gives T−N=2(T−3N),T-N=2(T-3N), so T−N=2T−6N,T-N=2T-6N, which simplifies to 5N=T.5N=T. Therefore TN=5.\frac{T}{N}=5. Thus, the correct answer is D.

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Concepts: ages · linear equation

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