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.

(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

[AI-generated answer — Bot GPT 3.5]

(a) Let x be the number of cars sold by Dealership A and y be the number of trucks sold by Dealership A. The equation for the total cars and trucks for Dealership A is x + y = 225.

(b) Let c be the number of cars sold by Dealership B and t be the number of trucks sold by Dealership B. The equation for the total cars and trucks for Dealership B is c + t = 300.

(c) Given that Dealership A sold a total of 225 cars and trucks, we can solve the equation x + y = 225 to find the number of cars sold by Dealership A. However, the value of y is not given, so we cannot determine the exact number of cars sold by Dealership A.

(d) Given that Dealership B sold half as many trucks as Dealership A, we can determine the number of trucks sold by Dealership B once we know the number of trucks sold by Dealership A. However, the number of trucks sold by Dealership A is not given in the problem statement, so we cannot calculate the number of trucks sold by Dealership B.

Answer 2

[AI-generated answer — Step-by-Step Bot]

(a) The equation for the total cars and trucks for Dealership A can be represented as:

Cars + Trucks = 225

(b) The equation for the total cars and trucks for Dealership B can be represented as:

Cars (B) + Trucks (B) = 300

(c) To find out how many cars Dealership A sold, we can substitute the value of Trucks from equation (a) into equation (b):

Cars (B) + 2 * (Cars (B)) / 2 = 300

Simplifying the equation:

Cars (B) + Cars (B) = 300

2 * Cars (B) = 300

Dividing both sides by 2:

Cars (B) = 150

Therefore, Dealership A sold a total of 150 cars.

(d) Given that Dealership B sold half as many trucks as Dealership A, we can substitute the value of Cars from equation (c) into equation (b):

Cars (B) + Trucks (B) = 300

150 + Trucks (B) = 300

Subtracting 150 from both sides:

Trucks (B) = 150

Therefore, Dealership B sold a total of 150 trucks.

Answer 3

[AI-generated answer — Explain Bot]

To solve this problem, we can use algebraic equations to represent the information given.

(a) Let's denote the number of cars sold by Dealership A as 'x' and the number of trucks as 'y'. The equation for Dealership A can be written as follows:

x + y = 225

(b) According to the information, 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 '2x' (twice as many as A) and the number of trucks sold by Dealership B as '0.5y' (half as many as A). The equation for Dealership B is:

2x + 0.5y = 300

(c) To find out how many cars Dealership A sold, we can substitute the values into equation (a) and solve for 'x':

x + y = 225

We don't have any specific information for 'y', so we'll need to solve this as a system of equations.

(d) Given that Dealership B sold half as many trucks as Dealership A, we can substitute the value of 'y' from equation (a) into equation (b) and solve for '0.5y':

2x + 0.5y = 300

Let's find the solutions to these equations.