Lizzy: Bill and Joan both work for a library. 5 years ago, Joan had 3 times as much experience as Bill. Now she has twice as much experience as Bill. How many years of experience does Bill have now?.
Me: Hmmm, let me think. I think this is the detailed solution:
Let b be Bill's years of experience and j be Joan's years of experience. We know that j - 5 = 3(b - 5) and j = 2b. Substituting the second equation into the first equation, we get 2b - 5 = 3(b - 5). Multiplying through the parentheses, we get 2b - 5 = 3b - 15. Adding 15 to both sides, we get 2b + 10 = 3b. Subtracting 2b from both sides, we get 10 = b. Final answer: 10.