Question

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. how many cars do the two dealerships sell in total

Answer 1

The two dealerships sell a total of 492 cars altogether. We determined this by solving a system of equations based on the information given about the number of cars and trucks sold at both dealerships.

Step-by-step explanation:

Let's denote the number of cars and trucks sold at the first dealership by C1 and T1, respectively, and the number of cars and trucks at the second dealership by C2 and T2, respectively. We are given:

C1 + T1 = 164

C2 + T2 = 229

C2 = 2 × C1

T2 = 0.5 × T1

Using substitution from the given information (C2 = 2 × C1, and T2 = 0.5 × T1), we can write the second equation as:

2 × C1 + 0.5 × T1 = 229

Now we need to solve the system of equations:

1. C1 + T1 = 164
2. 2C1 + 0.5T1 = 229

Multiplying the second equation by 2 yields:

1. 2C1 + T1 = 328

Subtracting the first original equation from this new equation, we get:

(2C1 + T1) - (C1 + T1) = 328 - 164

C1 = 164

Now we substitute C1 back into the first equation to find T1:

164 + T1 = 164

T1 = 0

With C1 found, we can now find C2:

C2 = 2 × 164 = 328

To find the total number of cars sold at both dealerships, we combine C1 and C2:

Total cars = C1 + C2 = 164 + 328 = 492

Therefore, the two dealerships sell a total of 492 cars.

Answer 2

294 cars.

Step-by-step explanation:

Let x be the number of cars and y be the number of trucks.

We have been given that the first dealership sells a total of 164 cars and trucks. We can represent this information as:

`x+y=164...(1)`

The second dealership sells twice as many cars and half as many trucks as the first dealership. So the number of cars sold by 2nd dealership will be 2x and number of trucks sold by 2nd dealership will be y/2.

Further, the 2nd dealership sold a total of 229 cars and trucks. We can represent this information as:

`2x+(y)/(2)=229...(2)`

We can see that total number of cars sold on two dealerships will be
`x+2x=3x`.

We will use substitution method to solve for x. From equation (1) we will get,

`y=164-x`

Substituting this value in equation (2) we will get,

`2x+(164-x)/(2)=229`

Now let us have a common denominator.

`(4x)/(2)+(164-x)/(2)=229`

`(4x+164-x)/(2)=229`

Upon multiplying both sides of our equation by 2 we will get,

`2* (4x+164-x)/(2)=2* 229`

`4x+164-x=458`

`4x+164-164-x=458-164`

`4x-x=458-164`

`3x=294`

Therefore, the total number of cars sold by two dealerships is 294.