Question 191762
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 $12480" translates to: {{{45x+30y=12480}}}





So we have the following system of equations


{{{x=2y}}}
{{{45x+30y=12480}}}





{{{45(2y)+30y=12480}}}  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+30y=12480}}} Distribute



{{{120y=12480}}} Combine like terms on the left side



{{{y=(12480)/(120)}}} Divide both sides by 120 to isolate y




{{{y=104}}} Divide





Now that we know that {{{y=104}}}, we can plug this into {{{x=2y}}} to find {{{x}}}




{{{x=2(104)}}} Substitute {{{104}}} for each {{{y}}}



{{{x=208}}} Multiply



So our answers are {{{x=208}}} and {{{y=104}}} which the ordered pair *[Tex \LARGE \left(202,101\right)]




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