Question

Using what you have learned about solving systems of equations, find the number that represents the apple, banana, and cherry.

Answer 1

`Apple \to 4`

`Banana \to 4`

`Cherry \to 5`

Explanation:

Given

`A \to Apple`

`B \to Banana`

`C \to Cherry`

From the rows, the equation is:

`B + 2A =12` --- (1)

`2B + C = 13` --- (2)

`A + 2C = 14` --- (3)

Make A the subject in:
`A + 2C = 14`

`A = 14 -2C`

Substitute
`A = 14 -2C` in
`B + 2A =12`

`B + 2(14 - 2C ) = 12`

`B + 28 - 4C = 12`

Make B the subject

`B = 4C - 28 +12`

`B = 4C -16`

Substitute
`B = 4C -16` in
`2B + C = 13`

`2(4C - 16) + C = 13`

`8C - 32 + C = 13`

Collect like terms

`8C + C = 13+32`

`9C = 45`

Divide by 9

`C = 5`

Recall that:

`B = 4C -16`

`B =4*5-16`

`B =20-16`

`B =4`

Recall that:

`A = 14 -2C`

`A= 14 -2*5`

`A= 14 -10`

`A =4`

Hence:

`Apple \to 4`

`Banana \to 4`

`Cherry \to 5`