SOLUTION: a log 78 feet is to be cut into three peices of varying lengths. The longest piece is to be 4 times the length of the shortest peice and the middle sized piece is to be 6 feet less

Question 216522: a log 78 feet is to be cut into three peices of varying lengths. The longest piece is to be 4 times the length of the shortest peice and the middle sized piece is to be 6 feet less than twice the length of the shortest piece. How long is the shortest piece?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
a log 78 feet is to be cut into three pieces of varying lengths.
The longest piece is to be 4 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 shortest piece?
:
Let x = length of the shortest piece
:
It says,"The longest piece is to be 4 times the length of the shortest piece"
therefore:
4x = the longest piece
:
"the middle sized piece is to be 6 feet less than twice the length of the shortest piece."
therefore:
(2x-6) = middle sized piece
:
How long is the shortest piece?
The sum of the three pieces is given as 78'
therefore:
x + (2x-6) + 4x = 78
x + 2x + 4x = 78 + 6
7x = 84
x =
x = 12' is the shortest piece
;
:
Check solution
4(12) = 48' is longest
2(12)-6 = 18' is the middle sized
sum
12 + 18 + 48 = 78
RELATED QUESTIONS
I am having issues with this word problem. NEED HELP! A log 78 feet long is to be cut... (answered by stanbon)

A log 78 feet long is cut into three pieces of varying lengths. The longest piece is to... (answered by stanbon)

a log 78 feet long is to be cut into three pieces of varying lengths. The longest piece... (answered by checkley77)

A log 78 feet long is to be cut into 3 pieces varying lengths. The longest piece is to be (answered by Paul)

becky has a board that is 2(3/4)feet long. she needs to cut the board into 11 peices of... (answered by hovuquocan1997)

A 45-foot rope is to be cut into three pieces. The second piece must be twice as long as... (answered by jim_thompson5910,Electrified_Levi)

a 24-inch board is to be cut into three piece so that the second piece is 3 times as long (answered by colliefan)

Translate the problem then solve: A 76 inch length of ribbon is to be cut into three... (answered by JulietG)

A 16inch board is to be cut into 3 peices so that the second peice is twice as long as... (answered by richard1234)