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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Mr. Hardin, the owner of two car dealerships in Lanberry, is holding a contest to see which one can sell the most cars. Lanberry Cars has already sold cars, and Hardin's Autos has sold cars. Going forward, the salespeople at Lanberry Cars think they can sell cars per day, whereas the salespeople at Hardin'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.
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Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Mr. Hardin, the owner of two car dealerships in Lanberry, is holding a contest to see which one can sell the most cars. Lanberry Cars has already sold cars, and Hardin's Autos has sold cars. Going forward, the salespeople at Lanberry Cars think they can sell cars per day, whereas the salespeople at Hardin'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. Lanberry Cars has already sold cars and will sell more cars per day. Hardin's Autos has already sold cars and will sell more cars per day.First equation based on Lanberry Cars: (total cars sold by Lanberry Cars after days)Second equation based on Hardin's Autos: (total cars sold by Hardin's Autos after days)
- Set Up Equations: Set up the system of equations to find when the two dealerships will have sold the same number of cars.Since both dealerships will have sold the same number of cars, we can set the expressions equal to each other:
- Solve Equation: Solve the equation for .Subtract from both sides:Subtract from both sides:Divide both sides by :
- Calculate Total Cars Sold: Calculate the total number of cars sold by each dealership after days.For Lanberry Cars: carsFor Hardin's Autos: cars
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