4800 divide by 3=1600 (2 cars 1 truck)
4600-1600=3000 (6 cars)
3000 divide by 3=1000 (2 cars)
1000×2=2000 (4 cars)
4800-2000=2800 (2 cars 3 trucks)
$2,800
Let [tex]x[/tex] be the number of cars sold.
Let [tex]y[/tex] be the number of trucks sold.
We know that a person selling 6 cars and 3 trucks earns $4,800, so:
[tex]6x+3y=4800[/tex] Equation (1)
We also know that a person selling 8 cars and 1 truck earns $4,600, so:
[tex]8x+y=4600[/tex] 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 [tex]y[/tex] in equation (2)
[tex]8x+y=4600[/tex]
[tex]y=4600-8x[/tex] Equation (3)
2. Replace equation (3) in equation (1) and solve for [tex]x[/tex]
[tex]6x+3y=4800[/tex]
[tex]6x+3(4600-8x)=4800[/tex]
[tex]6x+13800-24x=4800[/tex]
[tex]-18x=-9000[/tex]
[tex]x=\frac{-9000}{-18}[/tex]
[tex]x=500[/tex] Equation (4)
3. Replace equation (4) in equation (3) to find [tex]y[/tex]
[tex]y=4600-8x[/tex]
[tex]y=4600-8(500)[/tex]
[tex]y=4600-4000[/tex]
[tex]y=600[/tex]
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
