If x and y are positive integers for which 3x + 2y + xy = 115 + 11x + 2y, then what is x + y?

parmen Jul 30, 2024

#1**+1 **

mmm...not sure about my solution, but here it is.

First, let's combine all the like terms. Isolating 115, we get

\(-8x+xy=115\)

Now factoring out x from the left side, and isolating x, we find

\(x\left(y-8\right)=115\\ x=\frac{115}{y-8}\)

Now, I guess we want integers, so let's just see what y can be to make x an integer.

115 only has 2 factors other and 1 and itself: 5 and 23.

So x + y has 2 cases.

First, y could be 13, and x is 23.

The other option is for y to be 31, and x is 5.

So we have \(13+23=31+5=36\)

So the answer is 36.

Thanks! :)

NotThatSmart Jul 30, 2024