A company owns two dealerships, both of which sell cars and trucks. The first dealership sells a total of 164 cars and trucks. The second dealership sells twice as many cars and half as many trucks as the first dealership, and sells a total of 229 cars and trucks.

Question

An equation for the total cars and trucks for dealership A:

An equation for the total cars and trucks for dealership B:

How many cars did dealership A sell?

How many trucks did the dealership B sell?

Answer 1

Let's represent the number of cars sold by the first dealership as "C1" and the number of trucks as "T1".
Similarly, let's represent the number of cars sold by the second dealership as "C2" and the number of trucks as "T2".

From the problem, we have the following information:

C1 + T1 = 164 ..........(equation 1)

C2 + T2 = 229 ..........(equation 2)

We also know that the second dealership sells twice as many cars as the first dealership and half as many trucks as the first dealership. This can be expressed as:

C2 = 2C1 ..........(equation 3)

T2 = 0.5T1 ..........(equation 4)

To find the equation for the total cars and trucks for dealership A (C1 + T1), we can substitute equations 3 and 4 into equation 2:

2C1 + 0.5T1 = 229

Simplifying this equation, we get:

2C1 + 0.5T1 = 229

To find the equation for the total cars and trucks for dealership B (C2 + T2), we can substitute equations 3 and 4 into equation 2:

2C1 + 0.5T1 = 229

So, the equation for the total cars and trucks for dealership A is 2C1 + 0.5T1 = 229.

To find the number of cars sold by dealership A, we can substitute equations 3 and 4 into equation 1:

C1 + T1 = 164

Simplifying this equation, we get:

C1 + 0.5T1 = 164

We have two equations with two variables (C1 and T1), so we can solve them simultaneously.

Now, we need to solve the system of equations:

2C1 + 0.5T1 = 229 ..........(equation 5)
C1 + 0.5T1 = 164 ..........(equation 6)

We can eliminate T1 by multiplying equation 6 by -0.5 and adding it to equation 5.

-0.5(C1 + 0.5T1) + 2C1 + 0.5T1 = -0.5(164)

This simplifies to:

1.5C1 = -0.5(164)

1.5C1 = -82

Dividing both sides by 1.5 gives us:

C1 = -54

Since we cannot have a negative number of cars sold, this means there was an error in the problem statement or calculations.

As a result, we cannot determine the number of cars dealership A sold or the number of trucks dealership B sold based on the given information.