Skip to main content

2007 AMC 12B Problem 8

Problem 8 of 25EasierAlgebra

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}?

Answer choices

Show solution

Solution

Tom’s age NN years ago was T−N.T-N. His three children were each NN years younger, so their ages then totaled T−3N.T-3N. The condition gives T−N=2(T−3N), T-N=2(T-3N), so 5N=T5N=T and TN=5.\frac{T}{N}=5. Thus, the correct answer is D.

More practice

Concepts: ages · linear equation

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.