Question 252666
5a+2b=34
Answers could be a=6 and b=2
2b must be even but b can be even or odd.
so if 2b must be even then 5a must be even so a must be even since 5 is odd and 34 is even.
If you subtract an even number from an even number, you get an even number.
a must be less than 7 since 5*7=35 and both a and b must be positive.
But the answers are sums of a not a itself
10 is possible because 5*4+2*7=34
6+4=10

5*2+2*12=34
so we could have 6,4 and 2 for a total of 12
since 6, 4 and 2 are possible values for a 14 can't be since it would need 2 twice.
16 has a similar problem with 4
since we already have a sum of 12 a sum of 16 would need 4 again.
so the highest sum possible for a would be 12 using 2,4 and 6. We could also have a =0  and b would equal 17 but the sum of the a's would not change.