Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. Mr. Mason, the owner of two car dealerships in Fairfax, is holding a contest to see which one can sell the most cars. Fairfax Cars has already sold 19 cars, and Mason's Autos has sold 18 cars. Going forward, the salespeople at Fairfax Cars think they can sell 1 car per day, whereas the salespeople at Mason'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 many cars will each lot have sold? How long will that take?

Question

Mathematics

Eden Johnston

11 December, 09:58

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. Mr. Mason, the owner of two car dealerships in Fairfax, is holding a contest to see which one can sell the most cars. Fairfax Cars has already sold 19 cars, and Mason's Autos has sold 18 cars. Going forward, the salespeople at Fairfax Cars think they can sell 1 car per day, whereas the salespeople at Mason'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 many cars will each lot have sold? How long will that take?

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Answers (1)

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Camryn Fernandez · Answer 1

It will take one day and they will each sell 20 cars.

Step-by-step explanation:

Choose variables to represent each thing of interest:

Fairfax = F Mason = M days = d

F = 19 + 1 (d)

M = 18 + 2 (d)

The goal is for F and M to equal one another, so set the equations equal to one another.

19 + 1d = 18 + 2d

1 = d

So, it will take one day.

Now, solve for F and M

F = 19 + 1 (1) = 20

M = 18 + 2 (1) = 20