Question

write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
mr. pearson, the owner of two car dealerships in fairview, is holding a contest to see which one can sell the most cars. fairview cars has already sold 6 cars, and pearsons autos has sold 7 cars. going forward, the salespeople at fairview cars think they can sell 6 cars per day, whereas the salespeople at pearsons autos are aiming for sales of 5 cars per day. if the salespeoples predictions are accurate, it wont be long before the two dealerships are tied.
how many cars will each lot have sold? how long will that take?
the dealerships will each have sold □ cars in □ days.

Explanation:

Step1: Define variables

Let \( x \) be the number of days, and \( y \) be the number of cars sold.
For Fairview Cars: Initial cars sold = 6, cars sold per day = 6. So the equation is \( y = 6 + 6x \).
For Pearson's Autos: Initial cars sold = 7, cars sold per day = 5. So the equation is \( y = 7 + 5x \).

Step2: Set equations equal

To find when they are tied, set \( 6 + 6x = 7 + 5x \).

Step3: Solve for \( x \)

Subtract \( 5x \) from both sides: \( 6 + x = 7 \).
Subtract 6 from both sides: \( x = 1 \).

Step4: Find \( y \)

Substitute \( x = 1 \) into \( y = 6 + 6x \): \( y = 6 + 6(1) = 12 \).

Answer:

The dealerships will each have sold 12 cars in 1 day.