Let's assume Dealership A sold x cars and y trucks.
Therefore, given that Dealership A sold a total of 225 cars and trucks, we have:
x + y = 225 ..........(1)
Dealership B sold twice as many cars as Dealership A, i.e. 2x, and half as many trucks, i.e. y/2.
Therefore, given that Dealership B sold a total of 300 cars and trucks, we have:
2x + y/2 = 300 ..........(2)
Multiplying equation (1) by 2, we have:
2x + 2y = 450
Now subtracting this equation from equation (2), we get:
(2x + y/2) - (2x + 2y) = 300 - 450
y/2 - 2y = -150
Multiplying both sides by 2 to get rid of the fraction:
y - 4y = -300
-3y = -300
Dividing both sides by -3:
y = 100
Therefore, Dealership B sold 100 trucks.