SOLUTION: An 81 inches length of ribbon is to be cut into three pieces. The longest piece is to be 34 inches longer than the shortest piece, and the third piece is to be half the length of t

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: An 81 inches length of ribbon is to be cut into three pieces. The longest piece is to be 34 inches longer than the shortest piece, and the third piece is to be half the length of t      Log On


   

Question 771029: An 81 inches length of ribbon is to be cut into three pieces. The longest piece is to be 34 inches longer than the shortest piece, and the third piece is to be half the length of the longest piece. Find the length of each piece of ribbon.
Answer by Jc0110(165) About Me  (Show Source):
You can put this solution on YOUR website!
Let the first piece (longest) of ribbon to be x, the second piece (shortest) of ribbon to be y while the third piece of ribbon to be z.
x%2By%2Bz=81 --> Equation 1
x=y%2B34 --> Equation 2 ... Substitute x=y%2B34 into Equation 3
z=x%2F2 --> Equation 3
z=%28y%2B34%29%2F2
Substitute x=y%2B34 and z=%28y%2B34%29%2F2 into Equation 1.
%28y%2B34%29%2By%2B%28%28y%2B34%29%2F2%29=81
y%2B34%2By%2B%28y%2B34%29%2F2=81
2y%2B68%2B2y%2By%2B34=162
2y%2B2y%2By=162-68-34
5y=60
y=60%2F5
y=12
Substitute y=12 into Equation 2.
x=12%2B34
x=46
Substitute x=46 into Equation 3.
z=46%2F2
z=23
Therefore, the longest ribbon, x = 46 inches, the shortest ribbon, y = 12 inches and the third piece of ribbon, z = 23 inches.