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

Suppose a mango cost x dollar and a apple cost y dollar

there will be an binary system of equation

8*x+3*y=18
3*x+5*y=14.5

so soultions have to x=48/31     y=16/31

Let m= cost of mangoes 
a= cost of apples 
8m+3a=18 total (first equation)

3m+5a=14.50 (Second Equation)

Solve using system of equations

8m+3a=18.00
3m+5a=14.50
Multiply 1st equation by 5 and second equation by -3:
5(8m+3a)=5(18.00)
-3(3m+5a)=-3(14.50)
Your problem should look like:
40m+15a=90
-9m+-15a=-43.5
Then you cancel out the 15a and (-15a). So when you combine like terms you get: 31m=46.5 
Divide each side by 31. 
31m\31=46.5\31
m= 1.5
Then you plug in 1.5 into any of the original equation to find the cost of your apples.
3(1.5)+5a=14.5
4.5 + 5a = 14.5 
5a=14.5-4.5
5a=10
a=2
Each Mango cost $1.50 and each apple costs $2.00