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An 8ft board is cut into two pieces whose lengths are in the ratio 7:5. What is the number of inches in the length of the longer piece?
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lets call the length of the larger piece \(x\) so the length of the shorter piece is then \(8-x\) you know \(\frac{x}{8-x}=\frac{7}{5}\) so you can solve for \(x\)
cross multiply, get \[5x=7(8-x)\] and then solve the linear equation
5x=56-7x then +7x to each side is 12x=56 divide by 12 is about 4.6 . so the answer is 4.6 ?
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