Question 722233
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.