Question

A company owns two dealerships, both of which sell cars and trucks. Dealership A sells a total of 225 cars and trucks. Dealership B sells twice as many cars and half as many trucks as the Dealership A, and sells a total of 300 cars and trucks. (4 points) a) An equation for the total cars and trucks for Dealership A:

Answer 1

Let c be the number of cars and t be the number of trucks sold by Dealership A.
Then, from the given information, we have the equation:
c + t = 225.

Answer 2

Use your graphing calculator: Desmos Graphing Calculator A company owns two dealerships, both of which sell cars and trucks. Dealership A sells a total of 225 cars and trucks. Dealership B sells twice as many cars and half as many trucks as the Dealership A, and sells a total of 300 cars and trucks. (4 points) a) An equation for the total cars and trucks for Dealership A: x + y = 225 b) An equation for the total cars and trucks for Dealership B: c) How many cars did Dealership A sell? d) Given the fact that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?

Answer 3

b) An equation for the total cars and trucks for Dealership B:

Let c2 be the number of cars and t2 be the number of trucks sold by Dealership B.

From the given information, we know that Dealership B sells twice as many cars as Dealership A, so c2 = 2c.

Also, Dealership B sells half as many trucks as Dealership A, so t2 = 0.5t.

Therefore, the equation for the total cars and trucks for Dealership B is:

c2 + t2 = 300

Substituting the values of c2 and t2:

2c + 0.5t = 300

c) To find the number of cars sold by Dealership A, we can use the equation given in part a):

c + t = 225

Since we want to find the number of cars sold, we can isolate c:

c = 225 - t

Therefore, Dealership A sold 225 - t cars.

d) Given that Dealership B sold half as many trucks as Dealership A, we can use the equation for the total trucks of Dealership A:

t2 = 0.5t

So, Dealership B sold 0.5t trucks.