Answer
The quantity of $\$6.00/bu$ corn is $2700\;bu$
and the quantity of $\$15.00/bu$ corn is $450\;bu$.
Work Step by Step
Let the quantity of $\$6.00/bu$ corn is $x$
and the quantity of $\$15.00/bu$ corn is $y$.
Total quantity is $=3150\;bu$.
$\Rightarrow x+y=3150$ ...... (1)
Total selling price is $\$22,950$
$\Rightarrow 6x+15y=22,950$ ...... (2)
Multiply equation (1) by $-6$.
$\Rightarrow -6x-6y=-18,900$ ...... (3)
Add equation (2) and (3).
$\Rightarrow 6x+15y-6x-6y=22,950-18,900$
Simplify.
$\Rightarrow 9y=4050$
Divide both sides by $9$.
$\Rightarrow y=\frac{4050}{9}$
Simplify.
$\Rightarrow y=450$
Substitute the value of $y$ into equation (1).
$\Rightarrow x+450=3150$
Subtract $3150$ form both sides.
$\Rightarrow x=3150-450$
Simplify.
$\Rightarrow x=2700$
Hence, the quantity of $\$6.00/bu$ corn is $2700\;bu$
and the quantity of $\$15.00/bu$ corn is $450\;bu$.
