SOLUTION: Snookers Lumber can convert logs into either lumber or plywood. In a given day, the mill turns out twice as many units of plywood as lumber. It makes a profit of $30 on a unit of

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Snookers Lumber can convert logs into either lumber or plywood. In a given day, the mill turns out twice as many units of plywood as lumber. It makes a profit of $30 on a unit of      Log On


   

Question 146205: Snookers Lumber can convert logs into either lumber or plywood. In a given day, the mill turns out twice as many units of plywood as lumber. It makes a profit of $30 on a unit of lumber and $45 on a unit of plywood. How many of each unit must be produced and sold in order to make a profit of $12120?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=# of plywood boards, y=# of lumber

"In a given day, the mill turns out twice as many units of plywood as lumber" translates to x=2y

"It makes a profit of $30 on a unit of lumber and $45 on a unit of plywood. How many of each unit must be produced and sold in order to make a profit of $12120" translates to: 45x%2B30y=12120




So we have the following system of equations

x=2y
45x%2B30y=12120




45%282y%29%2B30y=12120 Plug in x=2y into the second equation. In other words, replace each x with 2y. Notice we've eliminated the x variables. So we now have a simple equation with one unknown.


90y%2B30y=12120 Distribute


120y=12120 Combine like terms on the left side


y=%2812120%29%2F%28120%29 Divide both sides by 120 to isolate y



y=101 Divide




Now that we know that y=101, we can plug this into x=2y to find x



x=2%28101%29 Substitute 101 for each y


x=202 Simplify


So our answer is x=202 and y=101 which also looks like



This means that they must sell 202 units of plywood and 101 units of lumber to obtain a profit of $12,120