SOLUTION: A 21-foot rope is cut into 2 pieces. Seven less than three times the length of the longer rope piece x is five times the length of the shorter piece, which is (21 − x) ft. Fi

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Question 1095495: A 21-foot rope is cut into 2 pieces. Seven less than three times the length of the longer rope piece x is five times the length of the shorter piece, which is (21 − x) ft. Find the length of the longer rope piece x (in ft). (Enter an exact number.)

Answer by mananth(16946) About Me  (Show Source):
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Let the length of the longer rope piece "x" . Then the length of the shorter piece is 21 - x
According to the problem,Seven less than three times the length of the longer rope piece x is five times the length of the shorter piece.
3x - 7 = 5(21 - x)
Simplifying and solving for x, we get:
3x - 7 = 105 - 5x
8x = 112
x = 14
Therefore, the longer rope piece has a length of 14 feet.