The product of two positive integers plus their sum is 95. The integers are relatively prime, and each is less than 20. What is the sum of the two integers?

1 answer

xy + x+y = 95
y(x+1) = 95-x
y = (95-x)/(x+1)

form ordered pairs with positive integer values of x and y

1 47 , y is too big
2 31 too big
3 23
4 * --- * = not an integer
5 15 yeahhhh
6 *
7 11 yeahhh
8 *
9 *

So far I found 2 such pairs
Take their sum in each case.

check for 7,11
product is 77 , sum = 18
What is 77 + 18?

Can you find some more ?