A company owns two dealerships, both of which sell cars and trucks. Dealership A sells a total of 164 cars and trucks. Dealership B sells twice as many cars and half as many trucks as Dealership A, and sells a total of 229 cars and trucks. (4 points) a) c) How many cars did Dealership A sell?

Question

A company owns two dealerships, both of which sell cars and trucks. Dealership A sells a total of 164 cars and trucks. Dealership B sells twice as many cars and half as many trucks as Dealership A, and sells a total of 229 cars and trucks. (4 points) a) c) How many cars did Dealership A sell?

Answer 1

Let's say the number of cars sold by Dealership A is x.

Dealership B sells twice as many cars as Dealership A, meaning it sold 2x cars.
Dealership A also sells trucks, which we'll represent as y.
Dealership B sells half as many trucks as Dealership A, meaning it sold 0.5y trucks.
The total number of cars and trucks sold by Dealership A is x + y = 164.
The total number of cars and trucks sold by Dealership B is 2x + 0.5y = 229.
From these two equations, we can create a system of equations:
x + y = 164
2x + 0.5y = 229
We can solve this system of equations. Let's multiply the first equation by 2 to eliminate the y variable:
2(x + y) = 2(164)
2x + 2y = 328
Now let's subtract the second equation from this result:
(2x + 2y) - (2x + 0.5y) = 328 - 229
2x + 2y - 2x - 0.5y = 99
1.5y = 99
Now we can isolate the y variable by dividing both sides by 1.5:
y = 99 / 1.5 = 66
Now we can substitute this value back into the first equation to solve for x:
x + 66 = 164
x = 164 - 66 = 98
Therefore, Dealership A sold 98 cars. Answer: \boxed{98}.

Answer 2

Let's assume the number of cars sold by Dealership A is C and the number of trucks sold by Dealership A is T.

Dealership A sells a total of 164 cars and trucks, so we can write the equation:
C + T = 164...................(1)

Dealership B sells twice as many cars as Dealership A, so the number of cars sold by Dealership B is 2C.
Dealership B sells half as many trucks as Dealership A, so the number of trucks sold by Dealership B is T/2.

Dealership B sells a total of 229 cars and trucks, so we can write the equation:
2C + T/2 = 229.................(2)

Let's solve this system of equations to find the number of cars sold by Dealership A (C).

First, let's multiply equation (2) by 2 to eliminate the fraction:
4C + T = 458...................(3)

Now, let's subtract equation (1) from equation (3) to eliminate T:
(4C + T) - (C + T) = 458 - 164
4C - C = 458 - 164
3C = 294

Dividing both sides of the equation by 3:
C = 294 / 3
C ≈ 98

Therefore, Dealership A sold approximately 98 cars.

Answer 3

To find out how many cars Dealership A sold, we can set up a system of equations based on the given information.

Let's assume the number of cars Dealership A sold is "c" and the number of trucks sold is "t".

From the given information, we know that:

Dealership A sold a total of 164 cars and trucks:
c + t = 164 (Equation 1)

Dealership B sold twice as many cars as Dealership A and half as many trucks:
2c + (1/2)t = 229 (Equation 2)

We can solve this system of equations to find the values of "c" and "t".

To solve the system, we can use the method of substitution or elimination.

Let's solve it using the method of elimination. We will multiply Equation 1 by -2 to eliminate the "c" term:

-2(c + t) = -2(164)
-2c - 2t = -328 (Equation 3)

Now we will add Equation 3 to Equation 2 to eliminate the "c" term:

(-2c - 2t) + (2c + (1/2)t) = -328 + 229
-2t + (1/2)t = -99
(-4/2)t + (1/2)t = -99
(-(4/2) + 1/2)t = -99
(-2 + 1)t = -99
(-1)t = -99
t = 99

Now we can substitute the value of "t" into Equation 1 to find the value of "c":

c + 99 = 164
c = 164 - 99
c = 65

Therefore, Dealership A sold 65 cars.