Let's define the variables first:

• Let $x$ represent the number of days it will take for the two dealerships to have sold the same number of cars.
• Let $y$ represent the total number of cars sold by each dealership at that time.

Now, we can write the system of equations based on the information provided:

1. For Oak Grove Cars: $y = 8 + 4x$ (They've already sold 8 cars and will sell 4 more cars per day.)

2. For Hensley's Autos: $y = 6 + 5x$ (They've already sold 6 cars and will sell 5 more cars per day.)

To solve this system using substitution, we can set the two expressions for $y$ equal to each other since both represent the total number of cars sold when the dealerships are tied.

$8 + 4x = 6 + 5x$

Now, solve for $x$:

$8 - 6 = 5x - 4x$ $2 = x$

So, it will take $x = 2$ days for the two dealerships to have sold the same number of cars.

Now substitute $x = 2$ back into either equation to find $y$. Let's use the equation for Oak Grove Cars:

$y = 8 + 4(2) = 8 + 8 = 16$

So, $y = 16$.

Final Answers:

• It will take 2 days for the two dealerships to have sold the same number of cars.
• At that time, each lot will have sold 16 cars.

Would you like more details or have any questions?

Related Questions:

1. What would happen if Oak Grove Cars could only sell 3 cars per day?
2. If Hensley's Autos increased their daily sales to 6 cars per day, how would that affect the outcome?
3. How many cars will each dealership have sold after 5 days if their sales rates remain unchanged?
4. If the initial sales were reversed (Oak Grove Cars sold 6 cars initially, and Hensley's Autos sold 8), how would the time to tie change?
5. What if a third dealership enters the contest, selling 4.5 cars per day and starting with 5 cars sold, how long until they tie with the others?

Tip: When dealing with systems of linear equations, substitution is a powerful method when one of the equations is easily solved for one variable.