2015 AMC 10A Problem 8

Let $p$ and $c$ be Pete’s and Claire’s current ages respectively. Then we have that $$p - 2 = 3(c - 2)$$ and $$p - 4 = 4(c - 4).$$ Simplifying both equations gives us $$p = 3c - 4$$ and $$p = 4c - 12.$$ Setting them equal, we have $$3c - 4 = 4c - 12$$$$c = 8.$$ This means that $$p = 3 \cdot 8 - 4 = 20.$$ Now, we need to find the number of years ($y$) until $$20 + y = 2(8 + y),$$ which gives us $$20 + y = 16 + 2y$$$$y = 4.$$ Thus, B is the correct answer.