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

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?

Answer 1

Let's assume the number of trucks Dealership B sold is x.

Dealership A sold twice the number of trucks, so it sold 2x trucks.
Dealership B sold half as many trucks as Dealership A, so it sold (1/2)*(2x) = x trucks.

The total number of trucks sold by both dealerships is x + x = 2x trucks.
According to the given information, the total number of trucks sold by both dealerships is 225.

So, we have the equation:
2x = 225

Now, we can solve for x:
x = 225/2
x = 112.5

Since the number of trucks sold must be a whole number, Dealership B sold 112 trucks.

Answer 2

Let's assume the number of trucks sold at Dealership A is T and the number of cars sold is C.

From the given information, we have C + T = 225. This can be rewritten as T = 225 - C. Equation (1)
We also know that the number of cars and trucks sold at Dealership B is twice the number of cars sold at Dealership A, or 2C.
In addition, Dealership B sold half as many trucks as Dealership A or T/2.
The total number of cars and trucks sold at Dealership B is T/2 + 2C = 300. Equation (2)
Since we have two equations and two unknowns (C and T), we can solve this simultaneous equation.
From equation (1), we can substitute 225 - C for T in equation (2). We get (225 - C)/2 + 2C = 300.
Next, we multiply through the equation by 2 to eliminate the fraction and simplify the equation: 225 - C + 4C = 600.
Combining like terms, we have 3C = 375.
Dividing by 3 gives us C = 125.
To find the number of trucks sold at Dealership B, we substitute the value of C = 125 back into equation (1):
T = 225 - C = 225 - 125 = 100.
Therefore, Dealership B sold 100 trucks. Answer: \boxed{100}.

Answer 3

To find out how many trucks Dealership B sold, we need to first determine how many cars and trucks Dealership A sold.

Let's assume the number of trucks sold by Dealership A is T, and the number of cars sold by Dealership A is C.

According to the given information, Dealership A sold a total of 225 cars and trucks. Therefore, we can write the equation as:

T + C = 225 (equation 1)

Now, let's look at Dealership B. It is mentioned that Dealership B sold twice as many cars and half as many trucks as Dealership A.

So, the number of trucks sold by Dealership B is T/2, and the number of cars sold by Dealership B is 2C.

The total number of cars and trucks sold by Dealership B is 300. So, we can write the equation as:

(T/2) + 2C = 300 (equation 2)

Now, we have two equations with two unknowns. We can solve these equations simultaneously to find the values of T (trucks sold by Dealership A) and C (cars sold by Dealership A).

Solve equations 1 and 2 simultaneously:
T + C = 225
(T/2) + 2C = 300

Multiply the first equation by 2 to eliminate T.

2T + 2C = 450 (equation 3)

Now, subtract equation 2 from equation 3.

2T + 2C - [(T/2) + 2C] = 450 - 300
2T + 2C - T/2 - 2C = 150

Combine like terms.

(4T + 4C - T - 4C)/2 = 150
(3T)/2 = 150

Multiply both sides by 2/3 to solve for T.

T = (2/3) * 150
T = 100

Now, we can substitute the value of T back into equation 1 to find the value of C.

100 + C = 225
C = 225 - 100
C = 125

So, Dealership A sold 100 trucks and 125 cars.

Since Dealership B sold half as many trucks as Dealership A,
Dealership B sold 100/2 = 50 trucks.

Therefore, Dealership B sold 50 trucks.