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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Mr. Lin, the owner of two car dealerships in Oakland, is holding a contest to see which one can sell the most cars. Oakland Cars has already sold cars, and Lin's Autos has sold cars. Going forward, the salespeople at Oakland Cars think they can sell cars per day, whereas the salespeople at Lin's Autos are aiming for sales of cars per day. If the salespeople's predictions are accurate, it won't 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.
Full solution
Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Mr. Lin, the owner of two car dealerships in Oakland, is holding a contest to see which one can sell the most cars. Oakland Cars has already sold cars, and Lin's Autos has sold cars. Going forward, the salespeople at Oakland Cars think they can sell cars per day, whereas the salespeople at Lin's Autos are aiming for sales of cars per day. If the salespeople's predictions are accurate, it won't 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.
- Define variables: Let's define the variables. Let be the number of days after which the two dealerships will have sold the same number of cars. Let be the total number of cars sold by each dealership when they are tied.
- First equation for Oakland Cars: Set up the first equation based on Oakland Cars. Oakland Cars has already sold cars and will sell more cars per day. So, the total number of cars sold by Oakland Cars after days will be .
- Second equation for Lin's Autos: Set up the second equation based on Lin's Autos. Lin's Autos has already sold cars and will sell more cars per day. So, the total number of cars sold by Lin's Autos after days will be .
- Set equations equal: Since we are looking for the point where the two dealerships have sold the same number of cars, we can set the two expressions equal to each other to find .
- Solve for x: Solve for x by rearranging the terms and isolating x.
- Find total cars sold: Now that we have the value of , we can find the total number of cars sold by each dealership when they are tied by substituting back into either the first or second equation. We'll use the first equation:
