Question

Mr. Mills, the owner of two car dealerships in Washington, is holding a contest to see which one can sell the most cars. Washington Cars has already sold 8 cars, and Mills's Autos has sold 14 cars. Going forward, the salespeople at Washington Cars think they can sell 4 cars per day, whereas the salespeople at Mills's Autos are aiming for sales of 2 cars per day. If the salespeople's predictions are accurate, it won't be long before the two dealerships are tied. How long will that take? How many cars will each lot have sold?

Answer 1

It will take 3 days for the two dealerships to be tied, and after 3 days, both dealerships will have sold a total of 20 cars.

Step-by-step explanation:

To find out how long it will take for the two dealerships to be tied, we can set up a system of equations to represent the number of cars sold at each dealership over time. Let x represent the number of days it will take for the two dealerships to be tied. The number of cars sold at Washington Cars will be 8 + 4x, and the number of cars sold at Mills's Autos will be 14 + 2x. Setting these two expressions equal to each other and solving for x, we get: 8 + 4x = 14 + 2x. Simplifying the equation, we get 2x = 6, which means x = 3. So, it will take 3 days for the two dealerships to be tied. Now, we can substitute this value of x back into one of the expressions to find the number of cars each dealership will have sold. For Washington Cars: 8 + 4(3) = 8 + 12 = 20 cars. And for Mills's Autos: 14 + 2(3) = 14 + 6 = 20 cars. Therefore, after 3 days, both dealerships will have sold a total of 20 cars.