SOLUTION: Hi, I'm kate and I need some help with linear systems. Snookers Lumber can convert logs into either lumber or plywood. In a given day the mill turns out twice as many units of pl

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Question 191762: Hi, I'm kate and I need some help with linear systems.
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. The mill makes a profit of $30 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 $12480. Thank-you for your help.
Found 2 solutions by RAY100, jim_thompson5910:
Answer by RAY100(1637) (Show Source):
You can put this solution on YOUR website!
30L + 45 P = 12480
but p=2l
30 L +45(2l) = 12480
30 L + 90 L =12480
120L=12480
L=104
p=2L = 208
check
30(104) + 45 ( 208) = 12480
12480 = 12480 ok

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 $12480" 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

Multiply

So our answers are and which the ordered pair

This means that they must sell 208 units of plywood and 104 units of lumber to obtain a profit of $12,480