A 100-foot rope is cut so that the shorter piece is
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17 May 2023, 02:11
Let the shorter piece of the rope be \(x\).
Longer piece will be \(100-x\).
We are told that the shorter piece is \(2/3\) rds the length of the longer piece, i.e.
\(x = \frac{2}{3}(100-x)\)
\(3x = 2(100-x)\)
\(3x = 200 - 2x\)
\(3x + 2x = 200\)
\(5x = 200\)
\(x = \frac{200}{5}\)
\(x = 40\)
The length of the shorter piece is \(40\) feet.
The Answer is D.
Check
The length of the shorter piece is \(40\) feet.
The length of the longer piece is \(100-x = 100-40 = 60\)
Lets check if the shorter piece is \(\frac{2}{3}\) rds of the longer piece
\(40 = (\frac{2}{3})60\)
\(40 = \frac{120}{3}\)
\(40 = 40\)
Hence we have the correct solution to the problem.