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.

An equation for the total cars and trucks for Dealership A

Answer 1

Let's represent the number of cars sold by Dealership A as 'C' and the number of trucks sold as 'T'.

According to the information given, Dealership A sells a total of 225 cars and trucks. So, the equation for the total cars and trucks sold by Dealership A can be written as:

C + T = 225

Answer 2

Let C be the number of cars sold by Dealership A and T be the number of trucks sold by Dealership A. We know that C + T = 225. Now we can solve for C in terms of T by using the information given in the problem.

Dealership B sells twice as many cars as Dealership A, so it sells 2C cars. Dealership B also sells half as many trucks as Dealership A, so it sells T/2 trucks. The total number of cars and trucks sold by Dealership B is 300, so we have the equation 2C + T/2 = 300.

Now we can solve this system of equations to find the value of C.

First, let's multiply the second equation by 2 to eliminate fractions:
2(2C) + (2)(T/2) = 2(300)
4C + T = 600

Next, let's subtract the first equation from the modified second equation:
4C + T - (C + T) = 600 - 225
3C = 375

Finally, divide both sides of the equation by 3 to solve for C:
C = 375/3
C = 125

Therefore, the equation for the total cars and trucks sold by Dealership A is C + T = 125 + T = 225.

Answer 3

To find the equation for the total cars and trucks sold at Dealership A, we can let "x" represent the number of cars and "y" represent the number of trucks sold.

We know that Dealership A sells a total of 225 cars and trucks. So, we can set up the equation:

x + y = 225

However, we also know that Dealership B sells twice as many cars and half as many trucks as Dealership A, and sells a total of 300 cars and trucks.

Let's use the given information to form another equation for Dealership B:

2x + (0.5y) = 300

Now we have a system of equations:
x + y = 225
2x + (0.5y) = 300

We can solve this system of equations to find the value of x and y, which will give us the equation for the total cars and trucks sold at Dealership A.