m = mangoes
a = apples
8m + 3a = 18 Equation 1
3m + 5a = 14.50 Equation 2
Lets multiply equation 1 by 5 and equation 2 by 3
The new equations are:
45m + 15a = 90
9m + 15a = 43.5
Subtract them and get:
36m = 46.5
m = 1.30 Divide both sides by 36
Substitute m into equation 2 (either is fine, but choose the easier one)
3(1.30) + 5a = 14.5
3.9 + 5a = 14.6 Expand the bracket
5a = 10.6 Minus both sides by 3.9
a = 2.12 Divide both sides by 5
Mangoes cost $1.30
Apples cost $2.12 (more like $2.10)
I feel that my working out is wrong, but that is how you work out the answer.