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

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) (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

"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:

So we have the following system of equations

Plug in into the second equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute

Combine like terms on the left side

Divide both sides by 120 to isolate y

Divide

Now that we know that , we can plug this into to find

Substitute for each

Simplify

So our answer is and 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

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