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. Given the fact that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?
Let's assume that the number of cars sold by Dealership A is c, and the number of trucks sold is t.
We know that c + t = 225.
Dealership B sold twice as many cars as Dealership A, so the number of cars sold by Dealership B is 2c.
Dealership B sold half as many trucks as Dealership A, so the number of trucks sold by Dealership B is t/2.
The total number of cars and trucks sold by Dealership B is 2c + t/2 = 300.
Combining these two equations, we get 2c + t/2 = 300
Multiplying both sides of the equation by 2 gives 4c + t = 600.
Subtracting c + t = 225 from the equation 4c + t = 600, we get 3c = 375.
Dividing both sides of the equation by 3 gives c = 125.
Putting this value in c + t = 225, we get 125 + t = 225
Subtracting 125 from both sides of the equation gives t = 225 - 125 = <<225-125=100>>100.
So, Dealership B sold 100 trucks. Answer: \boxed{100}.
To find out how many trucks Dealership B sold, let's start by finding the number of trucks sold by Dealership A.
We know that Dealership A sold a total of 225 cars and trucks. Let's assume the number of trucks sold by Dealership A is represented by 'x'.
So, Dealership A sold x trucks.
Now, we are given that Dealership B sold half as many trucks as Dealership A. Therefore, the number of trucks sold by Dealership B is (1/2)x.
We also know that Dealership B sold a total of 300 cars and trucks.
Therefore, the total number of trucks sold by Dealership B and Dealership A is: x + (1/2)x = 300.
Combining like terms, we have: (3/2)x = 300.
To solve for x, we can multiply both sides of the equation by (2/3) to isolate x:
(2/3)(3/2)x = (2/3)(300)
x = 200.
So, Dealership A sold 200 trucks.
Since Dealership B sold half as many trucks as Dealership A, Dealership B sold (1/2) * 200 = 100 trucks.
Let's solve this step by step.
Step 1: Let's represent the number of cars sold by Dealership A as "C_A" and the number of trucks sold by Dealership A as "T_A".
Step 2: According to the given information, Dealership A sold a total of 225 cars and trucks. So, we can set up the equation: C_A + T_A = 225.
Step 3: Dealership B sold twice as many cars as Dealership A, so we can represent the number of cars sold by Dealership B as "C_B" = 2 * C_A.
Step 4: Dealership B sold half as many trucks as Dealership A, so we can represent the number of trucks sold by Dealership B as "T_B" = 0.5 * T_A.
Step 5: According to the given information, Dealership B sold a total of 300 cars and trucks. So, we can set up the equation: C_B + T_B = 300.
Step 6: Substitute the expressions for C_B and T_B from steps 3 and 4 into the equation from step 5: 2 * C_A + 0.5 * T_A = 300.
Step 7: Simplify the equation from step 6: 2 * C_A + T_A/2 = 300.
Step 8: Now, we have a system of two equations:
C_A + T_A = 225,
2 * C_A + T_A/2 = 300.
Step 9: To solve the system of equations, we can multiply the first equation by 2 to eliminate T_A: 2 * C_A + 2 * T_A = 450.
Step 10: Subtract the equation from step 9 from the equation from step 8 to eliminate 2 * C_A: 2 * C_A + T_A/2 - (2 * C_A + 2 * T_A) = 300 - 450.
Step 11: Simplify the equation from step 10: -3/2 * T_A = -150.
Step 12: Solve for T_A by multiplying both sides by -2/3: T_A = -150 * (-2/3).
Step 13: Simplify the equation from step 12: T_A = 100.
Step 14: Substitute the value of T_A into the equation from step 2 to find C_A: C_A + 100 = 225.
Step 15: Solve for C_A: C_A = 225 - 100.
Step 16: Simplify the equation from step 15: C_A = 125.
Step 17: Substitute the values of C_A and T_A into the equation from step 4 to find T_B: T_B = 0.5 * 100.
Step 18: Simplify the equation from step 17: T_B = 50.
Therefore, Dealership B sold 50 trucks.