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. %0D%0A%0D%0A(4 points)%0D%0Aa) An equation for the total cars and trucks for Dealership A: %0D%0A%0D%0Ab) An equation for the total cars and trucks for Dealership B: %0D%0A%0D%0Ac) How many cars did Dealership A sell? %0D%0A%0D%0Ad) Given the fact that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?
a) Let's assume that the number of cars sold by Dealership A is C and the number of trucks sold is T. According to the problem, Dealership A sells a total of 225 cars and trucks. Therefore, the equation for the total cars and trucks sold by Dealership A is:
C + T = 225
b) Similarly, let's assume that the number of cars sold by Dealership B is X and the number of trucks sold is Y. According to the problem, Dealership B sells twice as many cars and half as many trucks as Dealership A, and sells a total of 300 cars and trucks. Therefore, the equation for the total cars and trucks sold by Dealership B is:
X + Y = 300
c) To find the number of cars sold by Dealership A, we can solve the equation C + T = 225. However, there is not enough information given in the problem to determine the specific number of cars sold by Dealership A.
d) Given the fact that Dealership B sold half as many trucks as Dealership A, we know that Y = T/2. To find the number of trucks sold by Dealership B, we can substitute this equation into the equation X + Y = 300:
X + T/2 = 300
However, without knowing the specific value of T, we cannot determine the number of trucks sold by Dealership B.
a) Let's represent the total cars and trucks sold by Dealership A as "x."
Therefore, the equation for Dealership A would be:
x = 225 (since it sells a total of 225 cars and trucks).
b) Let's represent the number of cars sold by Dealership B as "y."
And let's represent the number of trucks sold by Dealership B as "z."
According to the given information, Dealership B sells twice as many cars and half as many trucks as Dealership A. So, the equation for Dealership B would be:
y + z = 300 (since the total cars and trucks sold by Dealership B is 300).
c) To find out how many cars Dealership A sold, we look at the equation from part a:
x = 225
Therefore, Dealership A sold 225 cars.
d) Given that Dealership B sold half as many trucks as Dealership A, we can deduce that the number of trucks sold by Dealership B is half the number of trucks sold by Dealership A. So, the equation would be:
z = (1/2) * x
Since we know Dealership A sold 225 cars, we can substitute this value into the equation to find the number of trucks sold by Dealership B:
z = (1/2) * 225
z = 112.5
However, since we can't have a fraction of a truck, we round this number to the nearest whole number. Therefore, Dealership B sold 113 trucks.
a) To find an equation for the total cars and trucks sold at Dealership A, we need to consider that the total is 225. Let's represent the number of cars sold as "C" and the number of trucks sold as "T". Since the total is given by the sum of cars and trucks sold, the equation becomes:
C + T = 225
b) To find an equation for the total cars and trucks sold at Dealership B, we know that it sells twice as many cars and half as many trucks as Dealership A, with a total of 300. Let's represent the number of cars sold at Dealership B as "C2" and the number of trucks sold as "T2". The equation becomes:
C2 + T2 = 300
c) To find out how many cars Dealership A sold, we can use the equation from part (a). Rearranging the equation to solve for C, we have:
C = 225 - T
Since we don't have information about the number of trucks sold at Dealership A, we cannot precisely determine how many cars Dealership A sold. However, we can calculate the range of possibilities for the number of cars by considering different values for T (the number of trucks sold).
d) Given that Dealership B sold half as many trucks as Dealership A, we can represent the number of trucks sold at Dealership B as "T2" and the number of trucks sold at Dealership A as "T". The relationship between the two can be expressed as:
T2 = (1/2) * T
By substituting (1/2) * T for T2 in equation (b), we get:
C2 + (1/2) * T = 300
To determine the number of trucks that Dealership B sold, we need to know the value of T (the number of trucks sold at Dealership A), which is not provided in the given information. Without this value, we cannot calculate the number of trucks sold at Dealership B.