John has a piece of rope. The rope is 144 inches. He cuts the rope into three different pieces. One piece is 8 inches more than the shortest piece, and the longest piece is 13 inches longer than the shortest piece. What's the length of the longest piece?

The longest piece is 54 inches

Step-by-step explanation:

let the lengths of the ropes be x,y,z

let the length of the shortest pieces be x

A piece is 8 inches more than the shortest piece, i.e y=8+x

The longest  pieces is 13 inches longer than the shortest piece, i.e z=13+ x  

But the rope is 144 inches, i.e  x + y + z=144(1)

substitute y=8+x and z=13+x in equation (1)

x + 8+x + 13+ x =144

We can rearrange the equation, thus;

x+x+x +8+13=144

3x + 21 =144

subtract 21 from both-side of the equation

3x+21 -21 = 144-21

3x=123

Divide both-side of the equation by 3 to get the value of 3

3x/3 = 123/3

x = 41

The longest piece is z=13 + x

                                       =13 +41

                                        =54

Therefore the longest piece is 54 inches

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