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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Mr. Livingston, the owner of two car dealerships in Centerville, is holding a contest to see which one can sell the most cars. Centerville Cars has already sold cars, and Livingston's Autos has sold cars. Going forward, the salespeople at Centerville Cars think they can sell cars per day, whereas the salespeople at Livingston'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 long will that take? How many cars will each lot have sold?In days, the dealerships will each have sold cars.
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Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Mr. Livingston, the owner of two car dealerships in Centerville, is holding a contest to see which one can sell the most cars. Centerville Cars has already sold cars, and Livingston's Autos has sold cars. Going forward, the salespeople at Centerville Cars think they can sell cars per day, whereas the salespeople at Livingston'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 long will that take? How many cars will each lot have sold?In days, the dealerships will each have sold cars.
- Define Variables: Let represent the number of days, and represent the number of cars sold. For Centerville Cars: Initial cars sold , Rate of selling cars/day. Equation:
- Centerville Cars: For Livingston's Autos: Initial cars sold = , Rate of selling = cars/day. Equation:
- Livingston's Autos: Set the equations equal to find when the dealerships will have sold the same number of cars:
- Set Equations Equal: Solve for : Subtract from both sides:
- Solve for x: Subtract from both sides:
- Substitute : Divide both sides by :
- Final Result: Substitute back into one of the original equations to find : Using :
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