SOLUTION: The total length of three wilderness trails is 20km. The first trail is 1km shorter than the twice the length of the second trail. The third trail is 2km longer than the first. Fin

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Question 219389: The total length of three wilderness trails is 20km. The first trail is 1km shorter than the twice the length of the second trail. The third trail is 2km longer than the first. Find the length of each trail.
Found 2 solutions by rfer, likaaka:
Answer by rfer(16322) About Me  (Show Source):
You can put this solution on YOUR website!
2x-1=7
x=4
(2x-1)+2=9
-----------------
2x-1+x+2x-1+2=20
5x=20
x=4

Answer by likaaka(51) About Me  (Show Source):
You can put this solution on YOUR website!
you must set up a system of equations and begin by naming the trails ie.
x = length of trail 1
y = length of trail 2
z = length of trail 3
the lengths of all three trails equal 20km so x + y + z = 20
the first trail is 1km shorter than twice the second so x = 2y - 1
the third trail is 2km longer than the first so z = x + 2, however since the first trail is solved using the second trail we can substitute the value of x into this equation giving you z = 2y - 1 + 2
Here's the system of equations
x + y + z = 20
x = 2y - 1
z = 2y + 1
Substitute the x and the z into the first equation and solve for y
2y - 1 + y + 2y + 1 = 20
5y = 20
y = 4, so the length of the second trail is 4km
Given that solve for the other two lengths
x = 2(4) -1
x = 7, so the first trail is 7km
z = 2(4) + 1
Z = 9, so the third trail is 9km