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# A carpenter saws a board that is 22 feet long into two pieces. One piece is to be 1 foot longer than twice the length of the shorter piece. Find the length of each piece.

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\begin{align*} &{\text{Let x = length of one piece of wood}}\\ &{\text{Let y = 1 + 2x = length of the other piece of wood}}\\ &x + y = 22 && {\text{Equation}}\\ &x + 1 + 2x = 22 && {\text{Substitute the value of y}}\\ &3x + 1 = 22 && {\text{Combine like terms}}\\ &3x + 1 - 1 = 22 - 1 && {\text{Use subtraction property of equality}}\\ &3x = 21 && {\text{Simplify}}\\ &\dfrac{\cancel{3}x}{\cancel{3}} = \dfrac{21}{3} && {\text{Use division property of equality}}\\ &{\color{#4257b2}x = 7} && {\text{Simplify}}\\ &y = 1 + 2x && {\text{Find the value of y}}\\ &y = 1 + 2(7) && {\text{Substitute 7 for x}}\\ &y = 1 + 14 && {\text{Multiply}}\\ &{\color{#4257b2}y = 15} && {\text{Add}}\\ \end{align*}

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