Question

A car salesperson has already sold 30 cars this year. They sell an average of 13 cars per month. Another salesperson has already sold 50 cars this year. She sells an average of 11 cars per month. After how many months will the salespeople have sold the same number of cars?

Variables:
Let m represent the number of months.

Equation:
Select the correct values to write an equation to represent the situation.
1. First salesperson: _______
2. Second salesperson: _______
Choices:
a. m+2
b. m−2
c. 2m
d. m
Solve the Equation:
After how many months will the salespeople have sold the same number of cars?
m= _______ month(s).

Answer 1

The correct equation representing the situation is: m=10 months, and the correct choice from the given options is: d. m

Let's set up equations for both salespeople based on the information given.

The first salesperson has sold 30 cars already and sells an average of 13 cars per month. So, the total number of cars they sell after m months can be represented as 30+13m.

The second salesperson has sold 50 cars already and sells an average of 11 cars per month. So, the total number of cars they sell after m months can be represented as 50+11m.

To find out when they'll have sold the same number of cars, we'll set the two equations equal to each other:

30+13m=50+11m

Now, solve for m:

13m−11m=50−30

2m=20

m=10

So, after 10 months, both salespeople will have sold the same number of cars.

The correct equation representing the situation is: m=10 months, and the correct choice from the given options is: d. m