<h2>
Answer </h2>
$2,800
<h2>
Explanation</h2>
Let
be the number of cars sold.
Let
be the number of trucks sold.
We know that a person selling 6 cars and 3 trucks earns $4,800, so:
Equation (1)
We also know that a person selling 8 cars and 1 truck earns $4,600, so:
Equation (2)
Now, lets solve our system of equations (1) and (2) to find a much a person makes per car and truck sold
1. Solve for
in equation (2)
![8x+y=4600](https://tex.z-dn.net/?f=8x%2By%3D4600)
Equation (3)
2. Replace equation (3) in equation (1) and solve for ![x](https://tex.z-dn.net/?f=x)
![6x+3y=4800](https://tex.z-dn.net/?f=6x%2B3y%3D4800)
![6x+3(4600-8x)=4800](https://tex.z-dn.net/?f=6x%2B3%284600-8x%29%3D4800)
![6x+13800-24x=4800](https://tex.z-dn.net/?f=6x%2B13800-24x%3D4800)
![-18x=-9000](https://tex.z-dn.net/?f=-18x%3D-9000)
![x=\frac{-9000}{-18}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-9000%7D%7B-18%7D)
Equation (4)
3. Replace equation (4) in equation (3) to find ![y](https://tex.z-dn.net/?f=y)
![y=4600-8x](https://tex.z-dn.net/?f=y%3D4600-8x)
![y=4600-8(500)](https://tex.z-dn.net/?f=y%3D4600-8%28500%29)
![y=4600-4000](https://tex.z-dn.net/?f=y%3D4600-4000)
![y=600](https://tex.z-dn.net/?f=y%3D600)
Now we know that a person makes $500 per card sold and $600 per truck sold.
Commission earned by a person who sell 2 cars and 3 trucks:
2($500) + 3($600) = $1,000 + $1,800 = $2,800