Question

Greg has a piece of rope that is 18 ft long. He wants to cut it into two pieces so that the longer piece is 2 ft less than 3 times the length of the shorter piece. How long will each piece of rope be? Enter your answers in the boxes.

Answer 1

x - shorter piece
3x - 2 - longer piece

x + 3x -2 = 18
x + 3x = 18 +2
4x = 20 | : 4
x=5

3*5 -2 = 15 - 2 = 13
shorter piece: 5 ft
longer piece : 13 ft

I hope this helps

Answer 2

Answer : The length of the shorter and longer piece of the rope is, 5 ft and 13 ft respectively.

Step-by-step explanation :

Let the length of the shorter piece of rope be, 'x' ft.

Given:

Total length of the rope = 18 ft

Length of the longer piece = (18 - x) ft

and,

The longer piece is 2 ft less than 3 times the length of the shorter piece. That means,

`(18-x)=3x-2`

`18+2=3x+x`

`20=4x`

`x=(20)/(4)`

`x=5`

Thus, the length of the shorter piece of rope = x = 5 ft

The length of the longer piece of rope = (18 - x) ft = 18 - 5 = 13 ft

Hence, the length of the shorter and longer piece of the rope is, 5 ft and 13 ft respectively.