SOLUTION: A log 78 feet long is cut into three pieces of varying lengths. The longest piece is to be four times the length of the shortest piece, and the middle sized piece is to be 6 feet l

Question 223645: A log 78 feet long is cut into three pieces of varying lengths. The longest piece is to be four times the length of the shortest piece, and the middle sized piece is to be 6 feet less than twice the length of the shortest piece. How long is the longest piece?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A log 78 feet long is cut into three pieces of varying lengths. The longest piece is to be four times the length of the shortest piece, and the middle sized piece is to be 6 feet less than twice the length of the shortest piece. How long is the longest piece?
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Let the pieces be L,S,M for longest, shortest, and middle.
Equations:
L + S + M = 78
L = 4S
M = 2S-6
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Substitute for L and M and solve for "S":
4S + S + 2S-6 = 78
7S = 84
S = 12 ft
L = 4S = 48 ft
M = 2S-6 = 18 ft
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Cheers,
Stan H.
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