SOLUTION: a piece of fabric 180 inches long is cut into two pieces such that 3 times the larer piece exceeds 4 times the smaler piece by 85 inches.. how large are the pieces? I thought 3x+8

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: a piece of fabric 180 inches long is cut into two pieces such that 3 times the larer piece exceeds 4 times the smaler piece by 85 inches.. how large are the pieces? I thought 3x+8      Log On


   

Question 351952: a piece of fabric 180 inches long is cut into two pieces such that 3 times the larer piece exceeds 4 times the smaler piece by 85 inches.. how large are the pieces?
I thought 3x+85+4y = 180
but i have not clue. help me please its for my daughter shes 13 i want to get ths for her.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = length of larger piece and y = length of smaller piece


Since "a piece of fabric 180 inches long", this means that x%2By=180


Also, because the fabric "cut into two pieces such that 3 times the larer piece exceeds 4 times the smaler piece by 85 inches", this means that 3x=4y%2B85


x%2By=180 Start with the first equation.


y=180-x Subtract x from both sides.


3x=4y%2B85 Move onto the second equation


3x=4%28180-x%29%2B85 Plug in y=180-x


3x=720-4x%2B85 Distribute.


3x=-4x%2B805 Combine like terms on the right side.


3x%2B4x=805 Add 4x to both sides.


7x=805 Combine like terms on the left side.


x=%28805%29%2F%287%29 Divide both sides by 7 to isolate x.


x=115 Reduce.


y=180-x Go back to the previously isolated equation.


y=180-115 Plug in x=115


y=65 Subtract


So the solutions are x=115 and y=65 which means that the larger piece is 115 inches and the smaller piece is 65 inches long.


If you need more help, email me at jim_thompson5910@hotmail.com

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Jim