Question

12 apples and 8 guavas total cost is 76 pesos. 8 apples and 12 guavas cost 64 pesos. What is the cost of each apple and guava?

Answer 1

The cost of each apple and guava are 5 and 2 pesos respectively.

Explanation:

Let the cost of an apple be a and the cost a guava be g.

12a +8g= 76

Divide both sides by 4:

3a +2g= 19 -----(1)

8a +12g= 64

Divide both sides by 4:

2a +3g= 16 -----(2)

Let's solve the equations by elimination. Here, I will make the coefficients of the 'a' term equal in both equations, such that it can be eliminated so that I can solve for g.

(1) ×2:

6a +4g= 38 -----(3)

(2) ×3:

6a +9g= 48 -----(4)

(4) -(3):

6a +9g -(6a +4g)= 48 -38

Expand:

6a +9g -6a -4g= 10

5g= 10

g= 10 ÷5

g= 2

Substitute g= 2 into (1):

3a +2(2)= 19

3a +4= 19

3a= 19 -4

3a= 15

a= 15 ÷3

a= 5