SOLUTION: A 257 foot rope is cut into 4 pieces. The second piece is 3 feet longer than twice the shortest piece. The third piece is three times the length of the shortest piece. The last pie
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Question 262736: A 257 foot rope is cut into 4 pieces. The second piece is 3 feet longer than twice the shortest piece. The third piece is three times the length of the shortest piece. The last piece is 20 feet longer than half the shortest piece. How long is the longest piece? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! let a, b, c, d = the lengths of the 4 pieces, (d is the shortest)
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Write an equation for each statement:
:
"A 257 foot rope is cut into 4 pieces."
a + b + c + d = 257
:
"The second piece is 3 feet longer than twice the shortest piece."
b = 2d + 3
:
"The third piece is three times the length of the shortest piece."
c = 3d
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The last piece is 20 feet longer than half the shortest piece.(a is the only one left)
a = .5d + 20
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How long is the longest piece?
a + b + c + d = 257
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replace a, b, c using the above equations
(.5d+20) + (2d+3) + 3d + d = 257
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Combine like terms:
.5d + 2d + 3d + d + 20 + 3 = 257
:
6.5d + 23 = 257
:
6.5d = 257 - 23
:
6.5d = 234
d =
d = 36 ft is the shortest piece
then
a = .5(36) + 20
a = 18 + 20
a = 38
and
b = 2(36) + 3
b = 72 + 3
b = 75
and
c = 3(36)
c = 108, this would be the longest piece
:
:
Check solution
38 + 75 + 108 + 36 = 257
