Question

Mr. Adam, the owner of two car dealerships in Richie, is holding a contest to see which dealership can sell the most cars.

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​Richie Cars has already sold 3 cars, and Adam's Autos has sold 1 car. Going forward, the salespeople at Richie Cars think they can sell 1 car per day, whereas the salespeople at Adam's Autos are aiming for sales of 2 cars per day.
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​If the salespeople's predictions are accurate, it won't be long before the two dealerships are tied.
​At that point, how many cars will each dealership have sold?
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Graph a line to represent the number of cars sold for each dealership and then identify the answer by marking the point of intersection.
what would the two equations be?

Answer 1

The two equations representing the number of cars sold by each dealership are y = 3 + 1x for Richie Cars and y = 1 + 2x for Adam's Autos. The point of intersection between the two dealerships is (2, 5), which means they will be tied after 2 days.

Step-by-step explanation:

To find the point of intersection between the two car dealerships, we need to set up equations representing the number of cars sold by each dealership.

Let x represent the number of days since the contest started.

For Richie Cars, the equation is y = 3 + 1x, since they have already sold 3 cars and can sell 1 car per day.

For Adam's Autos, the equation is y = 1 + 2x, since they have already sold 1 car and can sell 2 cars per day.

To find the point of intersection, we set the two equations equal to each other and solve for x. 3 + 1x = 1 + 2x. Subtracting 1x from both sides gives 3 = 1 + x.

Subtracting 1 from both sides gives 2 = x.

So after 2 days, the two dealerships will be tied.

The graph representing the number of cars sold for each dealership will have Richie Cars' line with a y-intercept of 3 and a slope of 1 (ascending line), and Adam's Autos' line with a y-intercept of 1 and a slope of 2 (steeper ascending line).

Their lines will intersect at the point (2, 5).