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

Using What You Have Learned About Solving Systems Of Equations Find The Number That Represents The Apple Banana And Cherry class=

Sagot :

MrRoyalidn

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]

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