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a salesperson earns a commission based on the number and type of vehicle sold. a person selling 6 cars and trucks earns $4800. a person selling 8 cars and 1 truck earns $4600. how much does a salesperson earn for selling 2 cars and 3 trucks ?

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dunwbrooklyn

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) 

cerverusdante

Answer

$2,800

Explanation

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




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