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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Mr. Sheppard, the owner of two car dealerships in Greenwood, is holding a contest to see which one can sell the most cars. Greenwood Cars has already sold cars, and Sheppard's Autos has sold cars. Going forward, the salespeople at Greenwood Cars think they can sell cars per day, whereas the salespeople at Sheppard'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. Sheppard, the owner of two car dealerships in Greenwood, is holding a contest to see which one can sell the most cars. Greenwood Cars has already sold cars, and Sheppard's Autos has sold cars. Going forward, the salespeople at Greenwood Cars think they can sell cars per day, whereas the salespeople at Sheppard'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.
- Set up equations: Set up the equations to represent the number of cars sold by each dealership over time.Let represent the number of days after the contest starts, represent the number of cars sold by Greenwood Cars, and represent the number of cars sold by Sheppard's Autos. Greenwood Cars starts with cars sold and sells more per day. Sheppard's Autos starts with cars sold and sells more per day. The equations are: (for Greenwood Cars) (for Sheppard's Autos)
- Set equations equal: Since we want to find out when the two dealerships will have sold the same number of cars, we set the equations equal to each other.
- Solve for x: Solve for x by subtracting from both sides of the equation.
- Calculate : Subtract from both sides to solve for .
- Calculate z: Now that we have the number of days , we can find out how many cars each dealership will have sold. We can use either of the original equations for this, as they will both give us the same number of cars sold. Let's use the equation for Greenwood Cars.
- Confirm solution: To confirm our solution, we should also calculate using the number of days () to ensure it matches the number of cars sold by Greenwood Cars.
