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.
(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) Given the fact that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?
a) Let's say the number of cars sold by Dealership A is C and the number of trucks sold by Dealership A is T. Then, the equation for the total cars and trucks sold by Dealership A is C + T = 225.
b) Let's say the number of cars sold by Dealership B is C' and the number of trucks sold by Dealership B is T'. According to the given information, Dealership B sells twice as many cars as Dealership A, so C' = 2C. Also, Dealership B sells half as many trucks as Dealership A, so T' = T/2. Therefore, the equation for the total cars and trucks sold by Dealership B is C' + T' = 300.
c) Dealership A sells 225 cars based on the equation C + T = 225.
d) Given that Dealership B sold half as many trucks as Dealership A, we can substitute T' = T/2 into the equation C' + T' = 300 to get C + T/2 = 300. Since Dealership A sold 225 cars, we can substitute C = 225 into the equation to get 225 + T/2 = 300. Solving this equation gives T = 150. Therefore, Dealership B sold 150 trucks.
a) An equation for the total cars and trucks for Dealership A:
Let's assume the number of cars sold at Dealership A is C, and the number of trucks sold is T.
Since Dealership A sells a total of 225 cars and trucks, we can write the equation as:
C + T = 225
b) An equation for the total cars and trucks for Dealership B:
We know that Dealership B sells twice as many cars as Dealership A and half as many trucks. Let's assume the number of cars sold at Dealership B is C', and the number of trucks sold is T'.
Using this information, we can write the equation as:
C' + T' = 300
c) How many cars did Dealership A sell?
In the question, it states that Dealership A sells a total of 225 cars and trucks. So, we can use the equation from part a to find the number of cars sold at Dealership A.
C + T = 225
Since there is no specific information about the number of trucks sold at Dealership A, we cannot determine the exact number of cars sold. We can only determine the range of possible values based on the given information.
d) Given the fact that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?
We know that Dealership B sold half as many trucks as Dealership A. So, if Dealership A sold T trucks, Dealership B would sell T/2 trucks.
Using the equation from part b, we can substitute T/2 for T' to find the number of trucks sold at Dealership B.
C' + T/2 = 300
Again, without knowing the exact value of T, we cannot determine the exact number of trucks sold at Dealership B. We can only determine the range of possible values based on the given information.
a) Equation for the total cars and trucks for Dealership A:
Let's assume the number of cars sold by Dealership A is "C" and the number of trucks sold by Dealership A is "T". According to the given information, Dealership A sells a total of 225 cars and trucks.
So the equation for the total cars and trucks for Dealership A is:
C + T = 225
b) Equation for the total cars and trucks for Dealership B:
According to the given information, Dealership B sells twice as many cars and half as many trucks as Dealership A, and a total of 300 cars and trucks. Let's assume the number of cars sold by Dealership B is "C'" and the number of trucks sold by Dealership B as "T'".
The equation for the total cars and trucks for Dealership B is:
C' + T' = 300
c) How many cars did Dealership A sell?
From equation (a), we know that C + T = 225. Since C represents the number of cars sold by Dealership A, the number of cars sold by Dealership A is 225.
d) How many trucks did Dealership B sell?
Given the fact that Dealership B sold half as many trucks as Dealership A, we can deduce that T' = T/2. Substituting this into equation (b), we get:
C + (T/2) = 300
From equation (a), we know that C + T = 225. Rearrange it to T = 225 - C.
Substituting this value into equation (b), we get:
C + ((225 - C)/2) = 300
Simplifying this equation, we find:
C + (225 - C)/2 = 300
Multiplying through by 2, we get:
2C + 225 - C = 600
Simplifying further, we find:
C + 225 = 600
C = 600 - 225
C = 375
Therefore, Dealership A sold 375 cars, and since T = 225 - C, Dealership A sold T = 225 - 375 = -150 trucks. However, this result does not make sense in the given context, so there might be an error in the information provided or the calculation.