A farmer cuts a 300 feet fence into two pieces of different sizes. The longer piece is four times as long as the shorter piece. How long are the two pieces?

SOLUTION

Assume the length of the two pieces

Let the shorter piece be \(x\) feet. Then the longer piece must be \(4x\) feet.

Form an equation using total fence length(300ft) and solve for \(x\)

\(x + 4x = 300\)
⇒ \(5x = 300\)
⇒ \(x = 60\)

Find the lengths of the two pieces

shorter piece \( = x = 60\) feet
longer piece \( = 4x = 240\) feet

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Final Answer : The two pieces are 60ft and 240ft long.

Concept Note

Let the shorter piece be \(x\) ft and the longer piece be \(4x\) ft. Set up total length equation, solve for \(x\), and then find length of both pieces.