SOLUTION: A 85cm long rod is cut into 3 pieces. The longest piece is 3 times as long as the shortest piece and 13 cm longer than the remaining piece. What is the length of the longest piece?

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Question 722233: A 85cm long rod is cut into 3 pieces. The longest piece is 3 times as long as the shortest piece and 13 cm longer than the remaining piece. What is the length of the longest piece?

Please help! I dont know how to do the question but the answer is in the back of the book! My teacher didnt have time to explain how to do these types of questions
Thanks
Found 2 solutions by DrBeeee, htmentor:
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Don't try to remember questions - remember solution techniques.
Always define variables to represent the unknowns. Set up equations to fit the problem statement. Then solve the equations.
Let s = the shortest piece
Let L = the longest piece
Let r = the remaining piece
What do we know?
1) the three pieces add up to 85
2) L = 3*s
3) L = r + 13
Start with the basis of this type of problem that "the whole is equal to the sum of its parts" and get
(1) s + L + r = 85
We can eliminate r by using fact 3) and get
(2) r = L - 13.
Substitute r of (2) into (1) and get
(3) s + L + (L - 13) = 85 or
(4) s + 2*L = 85 + 13 or
(5) s + 2*L = 98
Now apply fact 2) to get
(6) s + 2*(3*s) = 98 or
(7) s + 6*s = 98 or
(8) 7*s = 98 or
(9) s = 14
Then from fact 2) we get
(10) L = 3*14 or
(11) L = 42 and
from (2) we get
(12) r = 42 - 13 or
(13) r = 29
Let's check using with (1).
Is (14 + 42 + 29 = 85)?
Is (85 = 85)? Yes
Answer: The longest piece is 42 cm.

Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
Let s, m and l represent the short, middle and long pieces, respectively
We have the following equations
s + m + l = 85 [sum of lengths]
l = 3s [longest three times as long as shortest]
l = m + 13 [longest is 13 cm longer than the middle piece]
Substitute l = 3s into the 1st and 3rd equation
s + m + 3s = 85
3s = m + 13 -> m = 3s - 13
s + (3s-13) + 3s = 85
7s = 98
s = 14
So l = 3s = 3*14 = 42
The longest piece is 42 cm