SOLUTION: A 20-ft board is cut into three pieces. The second piece is three times as long as the first. The third piece is twice as long as the second. Find the lengths of the pieces.

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Question 414352: A 20-ft board is cut into three pieces. The second piece is three times as long as the first. The third piece is twice as long as the second. Find the lengths of the pieces.
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A 20-ft board is cut into three pieces. The second piece is three times as long as the first. The third piece is twice as long as the second. Find the lengths of the pieces.
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There are 3 pieces: a,b,c
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Let 1st piece have length "x".
Then 2nd piece = "3x".
And 3rd piece is 2(3x) = "6x".
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Equation:
x + 3x + 6x = 20*12 inches
10x = 240 inches
x = 24 inches = 2 ft. (1st piece length)
3x = 6 ft (2nd piece length)
6x = 12 ft(3rd piece length)
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Cheers,
Stan H.
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Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

A 20-ft board is cut into three pieces: x, y and z
The second piece y is three times as long as the first x.
y=3x
The third piece z is twice as long as the second y.
z=2y=2%2A3x=6x
z=6x

Find the lengths of the pieces.
x%2By%2Bz=20ft........replace y and z with x

x%2B3x%2B6x=20ft...find x

10x=20ft

x=20ft%2F10
x=2ft..........now find y
y=3x
y=3%2A2ft
y=6ft..........now find z
z=6x
z=6%2A2ft
z=12ft

check:
x%2By%2Bz=20ft
2ft%2B6ft%2B12ft=20ft
20ft=20ft