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.
how many cars did dealership A sell
Let's say the number of cars dealership A sold is c, and the number of trucks sold is t.
We are told that c + t = 225...........(1) (the total number of cars and trucks sold by dealership A is 225).
Dealership B sells twice as many cars as dealership A, so the number of cars sold by dealership B is 2c.
Dealership B sells half as many trucks as dealership A, so the number of trucks sold by dealership B is (1/2)t.
We are also told that 2c + (1/2)t = 300...........(2) (the total number of cars and trucks sold by dealership B is 300).
Simplifying equation (2), we get 4c + t = 600.
From equation (1), we know that c = 225 - t.
Substituting this value of c into equation (2), we get 4(225 - t) + t = 600.
Expanding the brackets, we get 900 - 4t + t = 600.
Combining like terms, we get 900 - 3t = 600.
Subtracting 900 from both sides gives us -3t = -300.
Dividing both sides by -3, we get t = 100.
Now substituting this value of t into equation (1), we get c + 100 = 225.
Subtracting 100 from both sides gives us c = 225 - 100 = 125.
Therefore, dealership A sold 125 cars. Answer: \boxed{125}.
Dealership A sells a total of 225 cars and trucks.
To find out how many cars Dealership A sold, we first need to determine the number of cars sold by Dealership B. We know that Dealership B sold a total of 300 cars and trucks.
Given that Dealership B sold twice as many cars and half as many trucks as Dealership A, we can set up the following equations based on the information provided:
Let's say 'C' represents the number of cars sold by Dealership A, and 'T' represents the number of trucks sold by Dealership A.
Then we have the following equations:
Dealership B = 2 * Cars Sold by Dealership A
Dealership B = 0.5 * Trucks Sold by Dealership A
We know that Dealership B sold a total of 300 cars and trucks, so we can substitute the values into the equations:
300 = 2C
300 = 0.5T
Simplifying these equations gives us:
C = 300 / 2
C = 150
Therefore, Dealership A sold a total of 150 cars.