Answer:
[tex]Apple \to 4[/tex]
[tex]Banana \to 4[/tex]
[tex]Cherry \to 5[/tex]
Step-by-step explanation:
Given
[tex]A \to Apple[/tex]
[tex]B \to Banana[/tex]
[tex]C \to Cherry[/tex]
From the rows, the equation is:
[tex]B + 2A =12[/tex] --- (1)
[tex]2B + C = 13[/tex] --- (2)
[tex]A + 2C = 14[/tex] --- (3)
Make A the subject in: [tex]A + 2C = 14[/tex]
[tex]A = 14 -2C[/tex]
Substitute [tex]A = 14 -2C[/tex] in [tex]B + 2A =12[/tex]
[tex]B + 2(14 - 2C ) = 12[/tex]
[tex]B + 28 - 4C = 12[/tex]
Make B the subject
[tex]B = 4C - 28 +12[/tex]
[tex]B = 4C -16[/tex]
Substitute [tex]B = 4C -16[/tex] in [tex]2B + C = 13[/tex]
[tex]2(4C - 16) + C = 13[/tex]
[tex]8C - 32 + C = 13[/tex]
Collect like terms
[tex]8C + C = 13+32[/tex]
[tex]9C = 45[/tex]
Divide by 9
[tex]C = 5[/tex]
Recall that:
[tex]B = 4C -16[/tex]
[tex]B =4*5-16[/tex]
[tex]B =20-16[/tex]
[tex]B =4[/tex]
Recall that:
[tex]A = 14 -2C[/tex]
[tex]A= 14 -2*5[/tex]
[tex]A= 14 -10[/tex]
[tex]A =4[/tex]
Hence:
[tex]Apple \to 4[/tex]
[tex]Banana \to 4[/tex]
[tex]Cherry \to 5[/tex]
