Algebra Word Problem (Trouble Interpreting the Question)

Question

This is from a local contest that is already over:

The yearly salary increments received by a man equal the yearly salary increments received by his son. The man earned (yearly) 50% more than his son earned when the man earned what his son earns now. When the son earns what the man now earns, their combined salary will be 117000 dollars. How many dollars does the man now earn.

Based on my interpretation of the question (which may be wrong) So I assume that the increment can be denoted as y. So when they were the same age, the man earned 1.5x and the son earned x. I'm not sure how to approach as I'm not given the age difference. So, can I assume that the age difference is anything and that it will satisfy? For example, current salaries are x and 1.5x + 10y (where 10 years is the difference)?

Answer 1

Let the man's current salary be $m$, the son's be $s$, and the yearly increment be $y$. If the current year is $0$, in year $n$ the man makes $m+ny$ and the son makes $s+ny$. The year in which the man made as much as his son makes now is year $p$ ($p \lt 0$), where $m+py=s$ The second sentence then says $m+py=s=1.5(s+py)$. Since the increments are the same, if $-p$ years ago the man made what the son makes now, $-p$ years from now the son will make what the man makes now. So $m-py+s-py=117000$ We now have three equations in four unknowns, but $p$ and $y$ only appear as the product, so we can consider that one variable and we should be OK. $$m+py=s\\s=1.5(s+py)\\m-py+s-py=117000\\ s=-3py\\m=-4py\\-9py=117000\\py=-13000\\m=52000\\s=39000$$ Sorry about $p$ being negative. I got started that way.