Question 252889
You could plot this and then find all the points in the first quadrant with positive values for x. then total.

Or you could just grind it out. let's grind
a must be positive. So start with 1
Plug in 1 for a and solve for b {{{5*1 + b = 32}}} ---> {{{b= 32-5 = 27}}}
Plug in 2 for a. {{{10+b = 32}}} --> {{{b=22}}}
Plug in 3 for a. {{{15+b = 32}}} ---> {{{b= 17}}}
4 yields b = 12
5 yields b = 7
6 yields b = 2
7 yields b = -3

Since both a anfd b must be postive, then values for a are 1,2,3,4,5 and 6
Sum them to get 21