Question

If x and y are positive integers and x/5 + y/8 = 17/20, what is the value of
x + y?

Answer 1

x/5 + y/8 = 17/20
multiply by 40

8x + 5y = 34
y = (34-8x)/5

Since my numbers must be positive integers,
34-8x must be a multiply of 5
and furthermore x can only be 1,2,3, or 4
So we only have 4 numbers to try
if x=1 , y = 26/5 , no good
if x = 2, y = 18/5 , no good
if x = 3, y = 10/2 = 5 , yeahhhh!
if x = 4, y = 2/5 , no good

so x = 3, then y = 5
and x+y = 8