Monique 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 $1,800 that week. A second employee sells 6 cars and makes $2,050 that week.

Question

Part A- Write an equation in slope-intercept form, for the amount of money y a salesman will make in a week given the number of cars they sell in a week x.
Part B- How much will a salesman earn for selling 10 cars in one week?

Answer 1

To solve this problem, we need to find the commission per car sold and the base salary for the salesmen.

Part A

Let's denote:

• \( x \): the number of cars sold
• \( y \): the total earnings for the week

From the information provided, we can set up two equations based on the earnings of the two employees:

1. For the first employee who sells 5 cars and earns $1,800: \[ y = mx + b \implies 1800 = 5m + b \]

2. For the second employee who sells 6 cars and earns $2,050: \[ y = mx + b \implies 2050 = 6m + b \]

We now have a system of two equations:

1. \( 5m + b = 1800 \) (Equation 1)
2. \( 6m + b = 2050 \) (Equation 2)

Next, we can eliminate \( b \) by subtracting Equation 1 from Equation 2:

\[ (6m + b) - (5m + b) = 2050 - 1800 \] \[ m = 250 \]

Now that we have \( m \) (the commission per car), we can substitute \( m = 250 \) back into one of the equations to find \( b \). Using Equation 1:

\[ 5(250) + b = 1800 \] \[ 1250 + b = 1800 \] \[ b = 1800 - 1250 = 550 \]

Now we have both \( m \) and \( b \):

• Commission per car (\( m \)) = $250
• Base salary (\( b \)) = $550

Thus, the equation for the total earnings \( y \) in terms of the number of cars sold \( x \) is:

\[ y = 250x + 550 \]

Part B

To find out how much a salesman will earn for selling 10 cars in one week, we substitute \( x = 10 \) into the equation we just derived:

\[ y = 250(10) + 550 \] \[ y = 2500 + 550 \] \[ y = 3050 \]

Thus, a salesman will earn $3,050 for selling 10 cars in one week.