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.

Question

An equation for the total cars and trucks for Dealership
An equation for the total cars and trucks for Dealership
How many cars did Dealership A sell?
Given the fact that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?

Answer 1

Let's use variables to represent the number of cars and trucks sold by each dealership.

Let's say Dealership A sold x cars and y trucks. The total cars and trucks sold by Dealership A is x + y = 225.

Dealership B sold twice as many cars as Dealership A, which means it sold 2x cars. It also sold half as many trucks as Dealership A, so it sold 0.5y trucks. The total cars and trucks sold by Dealership B is 2x + 0.5y = 300.

To find the number of cars sold by Dealership A, we can solve the equation x + y = 225 for x:

x = 225 - y

Now we can substitute this into the equation for Dealership B:

2(225 - y) + 0.5y = 300

450 - 2y + 0.5y = 300

-1.5y = -150

y = -150 / -1.5

y = 100

So, Dealership A sold 225 - 100 = 125 cars.

And Dealership B sold 2(125) = 250 cars.

Dealership B also sold half as many trucks as Dealership A, so it sold 0.5 * 100 = 50 trucks.