SOLUTION: A farmer produced 750 bushels of a certain crop at a cost of $20 per bushel. If the farmer sold 2/3 of the bushels for double their production cost and sold the remaining bushels

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A farmer produced 750 bushels of a certain crop at a cost of $20 per bushel. If the farmer sold 2/3 of the bushels for double their production cost and sold the remaining bushels      Log On


   

Question 891968: A farmer produced 750 bushels of a certain crop at a cost
of $20 per bushel. If the farmer sold 2/3 of the bushels for
double their production cost and sold the remaining bushels
at 25 percent above their production cost, what was the
farmer’s gross profit on the sale of the crop?
Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
20%28%28+2%2F3+%2B+2%2F3+%2B+%28+1%2F3+%2B+%281%2F3%29%2A0.25+%29%29-1+%29
In the above, +2%2F3+%2B+2%2F3+ comes from the fact
that for each 2/3 bushel, sales covers the original
cost plus an additional 2/3 or double the production
cost.
For the remaining 1/3 bushel, sales cover the original
1/3 plus 25% of the 1/3.
Now, let's simplify
20%28%28+2%2F3+%2B+2%2F3+%2B+%28+1%2F3+%2B+%281%2F3%29%2A0.25+%29%29-1+%29
20%28%28+4%2F3++%2B+%28+1%2F3+%2B+1%2F12+%29%29-1+%29
20%28%28+4%2F3++%2B+%28+4%2F12+%2B+1%2F12+%29%29-1+%29
20%28%28+4%2F3++%2B+%28+5%2F12+%29%29-1+%29
20%28%28+16%2F12++%2B+%28+5%2F12+%29%29-1+%29
20%28%28+21%2F12++%29%29-12%2F12+%29
20%28%28+9%2F12++%29%29+%29
180%2F12
15
Notice that if the original expression,
20(( 2/3 + 2/3 + ( 1/3 + (1/3)*0.25 ))-1 )
is put into a calculator or solver we get 15.
Try entering into www.wolframalpha.com