Question

A rope is 24 feet long. It is cut into two pieces such that one piece is half the length of the other. Find the lengths of the two pieces of rope.

Let x = the length of the shorter piece of rope.

x + (1/2)x = 24

(3/2)x = 24
(2/3)(3/2)x = (2/3)

The stated solution is correct (lengths of 16 feet and 8 feet).

Based on the way the variable is defined, the equation should be x + 2x = 24.

The equation is written correctly, but there is an error in solving the equation.

The way the variable is defined, and because x=16, the longer piece of rope would be 32 feet, which is not possible.