SOLUTION: An 81 inch 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

Algebra ->  Linear-equations -> SOLUTION: An 81 inch 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      Log On


   

Question 1071293: An 81 inch 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
Found 2 solutions by josgarithmetic, Dirichlet:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Pieces, x y z

system%28x%2By%2Bz=81%2Cz=x%2B34%2Cy=z%2F2%29

The last two equations of the system can be expressed
system%28x=z-34%2Cand%2Cy=z%2F2%29
and you can substitute into the first equation of the system:

%28z-34%29%2Bz%2F2%2Bz=81
Solve this for z.
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Answer by Dirichlet(3) About Me  (Show Source):
You can put this solution on YOUR website!
The ribbon is to be divided into 3 pieces.
Let:
l = the length of the longest piece
s = the length of the shortest piece
t = the length of the third piece
So, we get:
81 = l + s + t
Given the info that the longest piece is to be 34 inches longer than the shortest piece. The generates the formula:
l = 34 + s
Given the info that the third piece is to be half the length of the longest piece. This generates the formula:
t = l / 2
Now, we plug l and t into our first formula. We get:
81 = (34 + s) + s + ((34 + s) / 2)
Simplifying, we get:
81 = 51 + 5s/2
Solving for s, we get s = 12.
Now, solve for l.
l = 34 + 12. l = 46.
Solve for t. t = 46/2. t = 23.
It checks! 46 + 23 + 12 = 81.