Question 146205
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+30y=12120}}}





So we have the following system of equations


{{{x=2y}}}
{{{45x+30y=12120}}}





{{{45(2y)+30y=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+30y=12120}}} Distribute



{{{120y=12120}}} Combine like terms on the left side



{{{y=(12120)/(120)}}} 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(101)}}} Substitute {{{101}}} for each {{{y}}}



{{{x=202}}} Simplify



So our answer is {{{x=202}}} and {{{y=101}}} which also looks like *[Tex \LARGE \left(202,101\right)]




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