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Use two equations in two variables to solve the application.A carpenter wants to cut a 15-foot board into two pieces so that one piece is 2 times as long as the other. How long (in ft) should each piece be?

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EXPLANATION

Assuming that x represents one piece and y the other, we can apply the following reasoning:

(1) x + y = 15

(2) y=2x

Plugging in y=2 into (1)

x + 2x = 15

Adding like terms:

3x = 15

Dividing both sides by 3:

x = 15/3

Simplifying:

x = 5

Substituting x=5 in (2):

y = 2*5 = 10

In conclusion, the first piece should be 5 ft long and the second one 10 ft.

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