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.

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]

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

According to the problem, Dealership A sells a total of 225 cars and trucks:

C + T = 225

Given that Dealership B sells twice as many cars and half as many trucks as Dealership A, we can represent the number of cars sold by Dealership B as "2C" and the number of trucks sold by Dealership B as "T/2".

The total number of cars and trucks sold by Dealership B is given as 300:

2C + T/2 = 300

To solve for C, we can express T in terms of C using the first equation:

T = 225 - C

Substituting this expression for T in the second equation, we have:

2C + (225 - C)/2 = 300

Multiplying through by 2 to eliminate the fraction, we get:

4C + 225 - C = 600

Combining like terms, we get:

3C = 375

Dividing both sides by 3, we find:

C = 125

Therefore, Dealership A sold 125 cars.

To find the number of trucks sold by Dealership B, we can substitute the value of C into the first equation:

125 + T = 225

Simplifying, we find:

T = 225 - 125 = 100

Therefore, Dealership B sold 100 trucks.

Answer 2

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

To find out how many cars Dealership A sold, we can use the information provided.

Dealership B sells twice as many cars as Dealership A, which means Dealership B sold 2 times the number of cars sold by Dealership A.

Dealership B sold a total of 300 cars and trucks.

Let's represent the number of cars sold by Dealership A as "x."

According to the given information, Dealership B sold 2 times the number of cars sold by Dealership A.

So, the number of cars sold by Dealership B is 2x.

Therefore, we can set up the equation:

x + 2x = 300

Combining like terms:
3x = 300

Now, we can solve for x by dividing both sides of the equation by 3:

3x/3 = 300/3
x = 100

Therefore, Dealership A sold 100 cars.

Now, let's move on to the next question.

Given the fact that Dealership B sold half as many trucks as Dealership A, we already know that Dealership A sold 225 cars and trucks in total.

Let's represent the number of trucks sold by Dealership A as "y."

According to the given information, Dealership B sold half as many trucks as Dealership A.

So, the number of trucks sold by Dealership B is 1/2 times the number of trucks sold by Dealership A.

Therefore, the number of trucks sold by Dealership B is (1/2) * y.

We know that Dealership A sold a total of 225 cars and trucks.

So, the equation becomes:

225 = y + (1/2) * y

To solve for y, we can simplify the equation:

225 = (3/2) * y

Multiplying both sides by 2/3:

(2/3) * 225 = (2/3) * y

150 = y

Therefore, Dealership B sold 150 trucks.

Answer 3

[AI-generated answer — Explain Bot]

To answer these questions, we need to use the information given about the sales of cars and trucks at both dealerships. Let's break down the problem step by step:

c) How many cars did Dealership A sell?

From the information given, we know that the total number of cars and trucks sold at Dealership A is 225. However, we don't know the specific breakdown between cars and trucks.

Let's assign variables for the number of cars sold at Dealership A (let's call it "Ca") and the number of trucks sold at Dealership A (let's call it "Ta"). Since we know that the total number of cars and trucks sold at Dealership A is 225, we can write an equation:

Ca + Ta = 225

However, we do not have enough information to solve for the individual values of Ca and Ta. This means we cannot determine the exact number of cars sold at Dealership A.

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

From the information given, we know that Dealership B sold twice as many cars as Dealership A (which we determined to be unknown) and half as many trucks as Dealership A. Let's use variables for the number of cars sold at Dealership B (Cb) and the number of trucks sold at Dealership B (Tb).

We know that Dealership B sold a total of 300 cars and trucks. So we can write another equation:

Cb + Tb = 300

We also know that Dealership B sold half as many trucks as Dealership A, which means Tb = (1/2) * Ta. Since we don't know the value of Ta, we cannot directly substitute it into this equation.

However, we can use the equation from part c (Ca + Ta = 225) to substitute Ta in terms of Ca:

Ta = 225 - Ca

Now we can substitute this expression for Ta in the equation for Dealership B:

Cb + (225 - Ca) = 300

Simplifying the equation:

Cb - Ca = 75

So, we have the equation Cb - Ca = 75 to relate the number of cars sold at Dealership B (Cb) to the number of cars sold at Dealership A (Ca). However, we cannot determine the exact values of Cb and Ca without additional information.

In conclusion, based on the given information, we cannot determine the exact number of cars sold at Dealership A (Ca) or the exact number of trucks sold at Dealership B (Tb).