A 24inch rope is to be cut into two pieces so that one piece

A 24-inch rope is to be cut into two pieces so that one piece is 8 inches longer than twice the other. How long is each piece, if a = 2, b = 8, and l = 24?

smaller piece

larger piece

Solution

ax+b+x=24

(a+1)x+b=24

Given a=2 and b=8

S0 , 3x+8 = 24

x = 16/3 inches.

So the smaller piece , x = 16/3 inches

Larger piece ,(2x+8) = 56/3 inches.