human
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?
assistant
How many years of experience does Joan have now? ** 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.
How many years of experience does Joan have now? ** Substituting the second equation into the first equation, we get 2b - 5 = 3(b - 5)
How many years of experience does Joan have now? ** Multiplying through the parentheses, we get 2b - 5 = 3b - 15
How many years of experience does Joan have now? ** Adding 15 to both sides, we get 2b + 10 = 3b
How many years of experience does Bill have now? ** Subtracting 2b from both sides, we get 10 = b
#### 10