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.

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) 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) Considering that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?

Answer 1

a) Let's represent the number of cars sold by Dealership A as 'x', and the number of trucks sold as 'y'. The total number of cars and trucks sold by Dealership A is given as 164. Therefore, the equation for the total cars and trucks for Dealership A can be written as:

x + y = 164

b) Let's represent the number of cars sold by Dealership B as '2x' (twice as many cars as Dealership A), and the number of trucks sold as 'y/2' (half as many trucks as Dealership A). The total number of cars and trucks sold by Dealership B is given as 229. Therefore, the equation for the total cars and trucks for Dealership B can be written as:

2x + (y/2) = 229

c) From equation (a), we know that x + y = 164.

To find the number of cars sold by Dealership A, we need to isolate the variable 'x'. Subtracting 'y' from both sides of the equation, we get:

x = 164 - y

d) Considering that Dealership B sold half as many trucks as Dealership A, we know that the number of trucks sold by Dealership B is equal to y/2.

Answer 2

a) Let's assume that the number of cars sold by Dealership A is C and the number of trucks sold by Dealership A is T. According to the problem, Dealership A sells a total of 164 cars and trucks. Therefore, the equation for the total cars and trucks for Dealership A is:

C + T = 164

b) Let's assume that the number of cars sold by Dealership B is C' and the number of trucks sold by Dealership B is T'. According to the problem, Dealership B sells twice as many cars as Dealership A and half as many trucks. Therefore, the equation for the total cars and trucks for Dealership B is:

C' + T' = 229

c) We know that Dealership A sells a total of 164 cars and trucks. From the equation in part a), we can substitute the value of T from equation b) into a):

C + (C' / 2) = 164

Now we can solve for C:

C + C' / 2 = 164
2C + C' = 328
C = 328 - C'

We don't have the value of C', so we can't determine the exact number of cars Dealership A sold. However, we can substitute different values for C' to find the corresponding values of C.

d) We are told that Dealership B sells half as many trucks as Dealership A. From the equation in part a), we can substitute the value of T from equation b) into a):

C + (T') / 2 = 164

Now we can solve for T':

T' / 2 = 164 - C
T' = 328 - 2C

We don't have the value of C, so we can't determine the exact number of trucks Dealership B sold.

Answer 3

a) An equation for the total cars and trucks for Dealership A:

Let's assume the number of cars sold by Dealership A is represented by "C" and the number of trucks sold by Dealership A is represented by "T". Since Dealership A sells a total of 164 cars and trucks, we can write the equation as:
C + T = 164

b) An equation for the total cars and trucks for Dealership B:
Dealership B sells twice as many cars as Dealership A, which means the number of cars sold by Dealership B is 2 times the number of cars sold by Dealership A. Similarly, Dealership B sells half as many trucks as Dealership A, which means the number of trucks sold by Dealership B is 0.5 times the number of trucks sold by Dealership A. Let's represent the number of cars sold by Dealership B as "C_B" and the number of trucks sold by Dealership B as "T_B". Considering the information provided, we can write the equation as:
C_B + T_B = 229
C_B = 2C
T_B = 0.5T

c) How many cars did Dealership A sell?
From the equation in part (a), C + T = 164, we can substitute the value of T from the equation in part (b), i.e., T = 2T_B, into the equation. This gives us:
C + 2T_B = 164
Since we don't have the exact values for C or T_B, we cannot solve for the exact number of cars Dealership A sold. However, we know that the total cars and trucks sold by Dealership A is 164.

d) Considering that Dealership B sold half as many trucks as Dealership A, we can substitute T_B = 0.5T into the equation from part (b):
C_B + 0.5T = 229
This equation does not provide enough information to solve for the exact number of trucks Dealership B sold.