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.

How many cars did Dealership A sell?

Answer 1

Let C be the number of cars sold by Dealership A.

Dealership B sells twice as many cars as Dealership A, so it sells 2C cars.
Dealership B sells half as many trucks as Dealership A, so it sells C/2 trucks.
Thus, Dealership B sells a total of C + 2C + C/2 = 300 cars and trucks.
Combining like terms, we get 5C/2 = 300
Multiplying both sides by 2/5, we get C = (2/5)*300 = <<2/5*300=120>>120 cars. Answer: \boxed{120}.

Answer 2

Let's assume that the number of cars sold by Dealership A is represented by "x" and the number of trucks sold by Dealership A is represented by "y".

We are given that Dealership A sells a total of 225 cars and trucks. Therefore, we can write the equation: x + y = 225.

Dealership B sells twice as many cars (2x) and half as many trucks (0.5y) as Dealership A. We are also given that Dealership B sells a total of 300 cars and trucks. Therefore, we can write the equation: 2x + 0.5y = 300.

Now, we can solve these two equations to find the values of x and y.

Using the first equation: x + y = 225, we can rewrite it as: y = 225 - x.

Substituting this value of y in the second equation, we get: 2x + 0.5(225 - x) = 300.

Simplifying the equation: 2x + 112.5 - 0.5x = 300.

Combining like terms: 1.5x + 112.5 = 300.

Subtracting 112.5 from both sides: 1.5x = 300 - 112.5.

Simplifying further: 1.5x = 187.5.

Dividing both sides by 1.5: x = 187.5 / 1.5.

Therefore, x = 125.

This means that Dealership A sold 125 cars.

Answer 3

To find out how many cars Dealership A sold, we need to use the information given in the question.

Let's denote the number of cars sold by Dealership A as "a" and the number of trucks sold as "t".

From the question, we know that the total number of cars and trucks sold by Dealership A is 225. So, we can write the first equation as:

a + t = 225 ...(1)

We also know that Dealership B sells twice as many cars as Dealership A and half as many trucks as Dealership A. Let's denote the number of cars sold by Dealership B as "b" and the number of trucks sold as "u".

From the question, we know that the total number of cars and trucks sold by Dealership B is 300. So, we can write the second equation as:

b + u = 300 ...(2)

We can also express the relationship between the number of cars and trucks sold by both dealerships using the given information. Dealership B sells twice as many cars as Dealership A, so we can write:

b = 2a ...(3)

Similarly, Dealership B sells half as many trucks as Dealership A, so we can write:

u = (1/2)t ...(4)

To solve these equations, we can use a method called substitution. Let's solve them step by step:

First, substitute the values of b and u from equations (3) and (4) into equation (2):

2a + (1/2)t = 300

Now, multiply the entire equation by 2 to eliminate the fraction:

4a + t = 600 ...(5)

Next, substitute the value of t from equation (1) into equation (5):

4a + (225 - a) = 600

Now, simplify the equation:

4a + 225 - a = 600

Combine like terms:

3a + 225 = 600

Subtract 225 from both sides of the equation:

3a = 375

Finally, divide both sides by 3 to solve for a:

a = 125

Therefore, Dealership A sold 125 cars.