Suppose you got 8 mangoes and 3 apples for $18 and 3 mangoes and 5 apples for $14.50.how many does each mango and each apple cost?

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.