Question

extra practice
write and solve equations with variables on each side
write and solve an equation for each exercise. check your solution. (examples
1 and 2)

1. a car salesperson has already sold 30 cars this year. he sells 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?
charges $20 per lesson plus a $30 fee for supplies. another
but charges $30 per lesson. after how

Explanation:

Step1: Define variable & set equation

Let $m$ = number of months. Total cars for first salesperson: $30 + 13m$. Total for second: $50 + 11m$. Set equal:
$$30 + 13m = 50 + 11m$$

Step2: Isolate variable terms

Subtract $11m$ from both sides:
$$30 + 2m = 50$$

Step3: Isolate constant terms

Subtract 30 from both sides:
$$2m = 20$$

Step4: Solve for $m$

Divide both sides by 2:
$$m = \frac{20}{2} = 10$$

Step5: Verify solution

Substitute $m=10$ into original equation:
Left side: $30 + 13(10) = 160$
Right side: $50 + 11(10) = 160$
Both sides are equal, so solution is valid.

Answer:

10 months