Question

A salesperson earns a commission based on the number and type of vehicle sold. A person selling 6 cars and 3 trucks earns $4,800. A person selling 8 cars and 1 truck earns $4,600. How much does a salesperson earn for selling 2 cars and 3 trucks?

a. $2,500.
b. $2,700.
c. $2,800.
d. $3,000.

Answer 1

c. $2.800

Explanation:

In this case we can solve it using a 2x2 system of equations, like this:

let x: value of cars

let y: value of trucks

So:

6 * x + 3 * y = 4800

8 * x + 1 * y = 4600 => y = 4600 - 8 * x

Replacing, we are left with that:

6 * x + 3 * (4600 - 8 * x) = 4800

6 * x + 13800 - 24 * x = 4800

6 * x - 24 * x = 4800 - 13800

-18 * x = -9000

x = -9000 / -18

x = 500

Now to calculate and:

y = 4600 - 8 * 500

y = 600

If selling 2 cars and 3 trucks, it would be:

2 * 500 + 3 * 600 = 2800

I would earn $ 2.800

Answer 2

C; $2,800

Explanation:

Let the amount earned per truck sales be $t and the amount earned per car sales be $c

Selling 6 cars and 3 trucks earned a total of $4,800

This mathematically means;

6c + 3t = $4,800 •••••••••(i)

Selling 8 cars and 1 truck earned a total of $4,600

This mathematically means;

8c + t = $4,600 ••••••••(ii)

Now, we solve both equations simultaneously;

From equation ii, t = 4600 -8c

we plug this in equation i

6c + 3(4600-8c) = 4,800

6c + 13,800 - 24c = 4,800

18c = 9000

c = 9,000/18

c = 500

in second equation;

t = 4,600 - 8c

inputing the value of c, we have;

t = 4,600 -8(500)

t = 4,600 - 4,000

t = 600

Now we want to know how much commission earned on selling 2 cars and 3 trucks.

That will be 2c + 3t = 2(500) + 3(600) = 1000 + 1,800 = $2,800