A 93 foot rope is to be cut into two pieces. One piece must be half as long as the other.  How long should the shorter piece be?

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Let x = one piece of rope.  Let x/2 be the shorter piece. x + x/2 = total length = 93 Multiply the first x term by 2/2 to get 2x/2 2x/2 +x/2 = (2x +x) /2 = 3x/2 = 93 Multiply both sides by 2 3x = 186                              divide both sides by 3 x = 62 ft       and the short rope is therefore 31 ft

Let the shorter piece of rope= xThe longer= 2x2x+x= 933x= 93x= 31The shorter piece of rope is 31 feet long. The longer piece of rope is 62 feet long.

31 and 6