Question

Morgan owns a car dealership in which her employees earn commission for each car they sell in addition to a weekly salary. One employee sells 5 cars and makes $1,875 that week. A second employee sells 6 cars and makes $2,150 that week.

Enter an equation, in slope-intercept form, for the amount of money y
an employee will make in a week given the number of cars sold x
.

Answer 1

To find the equation in slope-intercept form \( y = mx + b \), where \( y \) represents the total earnings, \( x \) represents the number of cars sold, \( m \) is the slope (the commission earned per car sold), and \( b \) is the weekly salary.

Let's denote:
- \( y_1 = 1875 \) when \( x_1 = 5 \) (for the first employee)
- \( y_2 = 2150 \) when \( x_2 = 6 \) (for the second employee)

We can set up a system of equations based on the given information:

1. \( 1,875 = m \cdot 5 + b \)
2. \( 2,150 = m \cdot 6 + b \)

To solve these equations, we can start by eliminating \( b \):

From the first equation:
\[
b = 1875 - 5m
\]

Now, substitute \( b \) into the second equation:
\[
2150 = 6m + (1875 - 5m)
\]

This simplifies to:
\[
2150 = 6m + 1875 - 5m
\]
\[
2150 = m + 1875
\]
\[
m = 2150 - 1875 = 275
\]

Now that we have the value of \( m \), we can substitute it back to find \( b \):
\[
b = 1875 - 5 \cdot 275
\]
\[
b = 1875 - 1375 = 500
\]

Now, we have \( m = 275 \) and \( b = 500 \). The equation in slope-intercept form is:
\[
y = 275x + 500
\]

Therefore, the equation representing the earnings of an employee based on the number of cars sold is:
\[
\boxed{y = 275x + 500}
\]

Answer 2

How much will an employee earn for selling 10 cars in one week? Enter the answer.

Answer 3

To find out how much an employee will earn for selling 10 cars in one week, we can use the equation we derived earlier:

\[
y = 275x + 500
\]

where \( x \) is the number of cars sold. We will substitute \( x = 10 \) into the equation:

\[
y = 275(10) + 500
\]
\[
y = 2750 + 500
\]
\[
y = 3250
\]

Therefore, an employee will earn **$3,250** for selling 10 cars in one week.