Question

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

Answer 1

Answer:

$Apple \to 4$

$Banana \to 4$

$Cherry \to 5$

Step-by-step 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:

$Apple \to 4$

$Banana \to 4$

$Cherry \to 5$