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? Given the fact that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?
Let's call the number of cars Dealership A sold x.
Dealership B sold twice as many cars as Dealership A, so Dealership B sold 2x cars.
Dealership A and B together sold a total of 225 +300 = <<225+300=525>>525 cars and trucks.
The total number of trucks Dealerships A and B sold is 525 - x - 2x = 525 - 3x.
Dealership B sold half as many trucks as Dealership A, so 525 -3x = x/2.
That means Dealership A sold 2(525-3x) = 1050-6x cars.
This means that 1050 - 6x = x.
Thus 1050 = 7x
Thus the x = 150 cars.
Thus Dealership A sold 150 cars and Dealership B sold 2(150)= <<2*150=300>>300 cars.
Dealership B sold half as many trucks as Dealership A, so Dealership B sold 150/2 = <<150/2=75>>75 trucks. Answer: \boxed{75}.
To find out how many cars Dealership A sold, we need to first determine the number of cars sold by Dealership B.
We know that Dealership B sold a total of 300 cars and trucks, and twice as many cars as Dealership A. So, let's find out how many cars Dealership B sold.
Since Dealership B sold twice as many cars as Dealership A, we can divide the total number of cars sold by Dealership B, which is 300, by 2.
300 / 2 = 150
So, Dealership B sold 150 cars.
Since Dealership A and Dealership B together sold a total of 225 cars and trucks, we can now find out how many cars Dealership A sold.
To do this, we simply subtract the number of cars sold by Dealership B from the total number of cars sold.
225 - 150 = 75
Therefore, Dealership A sold 75 cars.
Given the fact that Dealership B sold half as many trucks as Dealership A, we can determine the number of trucks sold by Dealership B.
To do this, we divide the number of trucks sold by Dealership A by 2.
75 / 2 = 37.5
Since we are dealing with whole numbers, we can round down to the nearest whole number, which is 37.
Therefore, Dealership B sold 37 trucks.
Let's find the number of cars Dealership A sold first. We know that Dealership B sold twice as many cars as Dealership A, which means Dealership B sold 2 * Cars(A) = 300 - Trucks(B) cars.
We also know that the total number of cars and trucks sold by Dealership A is 225, so Cars(A) + Trucks(A) = 225.
By substituting Cars(A) = 225 - Trucks(A) in the equation Cars(B) = 300 - Trucks(B), we can solve for Trucks(A).
300 - Trucks(B) = 2 * (225 - Trucks(A))
300 - Trucks(B) = 450 - 2 * Trucks(A)
-2 * Trucks(A) + Trucks(B) = 150
Now we can use this equation to solve for Trucks(A).
Since we know that Dealership B sold half as many trucks as Dealership A, we can write Trucks(B) = 0.5 * Trucks(A).
By substituting Trucks(B) = 0.5 * Trucks(A) into the equation -2 * Trucks(A) + Trucks(B) = 150, we can solve for Trucks(A).
-2 * Trucks(A) + 0.5 * Trucks(A) = 150
-1.5 * Trucks(A) = 150
Trucks(A) = 150 / -1.5
Trucks(A) = -100
Since the number of trucks can't be negative, there must be an error in the problem statement.
To answer the original question, we don't have enough information to determine how many cars Dealership A sold.