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 at Dealership A.

Let y be the number of trucks sold at Dealership A.
The equation for the total cars and trucks for Dealership A is:
x + y = 225

b) Let a be the number of cars sold at Dealership B.
Let b be the number of trucks sold at Dealership B.
The equation for the total cars and trucks for Dealership B is:
a + b = 300

c) From the equation in part a, we know that x + y = 225.
Since we are only interested in the number of cars sold at Dealership A, we need to isolate x.
Subtracting y from both sides of the equation gives:
x = 225 - y

d) Given that Dealership B sold half as many trucks as Dealership A, we can use y as the number of trucks sold at Dealership A to determine the number of trucks sold at Dealership B.
If Dealership A sold y trucks, Dealership B sold half as many trucks, which is y/2.
Therefore, Dealership B sold y/2 trucks.

Answer 2

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

To answer these questions step-by-step:

a) Let's assume the number of cars Dealership A sold is represented by 'x', and the number of trucks is represented by 'y'. Since the dealership sold a total of 225 cars and trucks, the equation is:
x + y = 225

b) Dealership B sells twice as many cars and half as many trucks as Dealership A. Let's assume the number of cars Dealership B sold is represented by 'm', and the number of trucks is represented by 'n'. Since the dealership sold a total of 300 cars and trucks, the equation is:
m + n = 300

c) We already know that Dealership A sold a total of 225 cars and trucks. So, we substitute the given values into the equation from part a:
x + y = 225
x + y = 225
225 + y = 225
y = 0
Therefore, Dealership A sold 0 trucks.

d) Dealership B sold half as many trucks as Dealership A, which means that the number of trucks Dealership B sold is half of the number of trucks Dealership A sold. We know that Dealership A sold 0 trucks, so Dealership B sold:
0 / 2 = 0 trucks.
Therefore, Dealership B sold 0 trucks.

Answer 3

[AI-generated answer — Explain Bot]

a) Let's denote the number of cars sold by Dealership A as "C_A" and the number of trucks sold by Dealership A as "T_A". According to the given information, Dealership A sold a total of 225 cars and trucks. Therefore, the equation for the total number of cars and trucks sold by Dealership A is:

C_A + T_A = 225

b) Similarly, let's denote the number of cars sold by Dealership B as "C_B" and the number of trucks sold by Dealership B as "T_B". According to the given information, Dealership B sold twice as many cars as Dealership A (2C_A) and half as many trucks as Dealership A (0.5T_A). The total number of cars and trucks sold by Dealership B is 300. Therefore, the equation for the total number of cars and trucks sold by Dealership B is:

2C_A + 0.5T_A = 300

c) To find the number of cars sold by Dealership A, we can rearrange equation (a) to solve for C_A:

C_A = 225 - T_A

d) According to the given information, Dealership B sold half as many trucks as Dealership A (0.5T_A). The equation for the number of trucks sold by Dealership B is:

T_B = 0.5T_A