Question

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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.
(4 points)

a) An equation for the total cars and trucks for Dealership A:

b) An equation for the total cars and trucks for Dealership B:

c) How many cars did Dealership A sell?

d) Given the fact that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?

Answer 1

a) Let's use the variable "x" to represent the number of cars sold by Dealership A, and "y" to represent the number of trucks sold by Dealership A. Since the total cars and trucks sold by Dealership A is 225, we can write the equation:

x + y = 225

b) Let's use the variable "m" to represent the number of cars sold by Dealership B, and "n" to represent the number of trucks sold by Dealership B. Since Dealership B sells twice as many cars and half as many trucks as Dealership A, we can write the equations:

m = 2x (twice as many cars)
n = 0.5y (half as many trucks)

The total cars and trucks sold by Dealership B is 300, so we can write another equation:

m + n = 300

c) From equation (a) we have x + y = 225. We can solve this equation to find the value of x (the number of cars sold by Dealership A). Since we don't have any specific values given in the problem, we cannot determine the exact number of cars sold by Dealership A without additional information.

d) Given that Dealership B sold half as many trucks as Dealership A, we can express the equation as:

n = 0.5y

From equation (a), we have y = 225 - x. Substituting this into the equation for Dealership B, we get:

n = 0.5(225 - x)

Again, since we don't have specific values for x, we cannot determine the exact number of trucks sold by Dealership B without additional information.