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

An equation for the total cars and trucks for Dealership A

Answer 1

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.