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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? ◆ B sell? î d) Given the fact that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership
a) Let's assume "C" represents the number of cars and "T" represents the number of trucks. For Dealership A, the equation would be:
C + T = 225
b) For Dealership B, it states that they sell twice as many cars as Dealership A and half as many trucks. Let's use the variables "C2" for the number of cars in Dealership B and "T2" for the number of trucks in Dealership B. The equation would be:
C2 + T2 = 300
c) To find out how many cars Dealership A sold, we need to solve for "C" in the equation from part a):
C + T = 225
C = 225 - T
Since we don't have the specific number of trucks sold by Dealership A, we cannot determine the exact number of cars sold by Dealership A.
d) The question states that Dealership B sold half as many trucks as Dealership A. Using the equations from parts a) and b), we can substitute the expressions for "C" and "T" in the equation for Dealership A:
C2 + T2 = 300
C2 + (225 - T) = 300
C2 - T = 75
Now, we have two equations:
C + T = 225
C2 - T = 75
Unfortunately, with only these two equations, we cannot determine the exact number of trucks sold by Dealership A or Dealership B.
a) Let's assume that the number of cars sold by Dealership A is represented by "x" and the number of trucks sold by Dealership A is represented by "y". The equation for the total cars and trucks sold by Dealership A can be written as:
x + y = 225 (Equation 1)
b) For Dealership B, it is given that they sold twice as many cars as Dealership A and half as many trucks as Dealership A. Using this information, we can write the equation for the total cars and trucks sold by Dealership B as:
2x + (1/2)y = 300 (Equation 2)
c) To find the number of cars sold by Dealership A, we need to solve Equation 1. Since the equation already includes both the car and truck sales, we can substitute the value of "y" from Equation 1 into Equation 2 and solve for "x".
x + (225 - x) = 225
225 = 2x + (1/2)(225 - x)
450 = 4x + 225 - x/2
225 = 7x - x/2
450 = 14x - x
450 = 13x
x = 450/13
x ≈ 34.62
So, Dealership A sold approximately 34.62 cars.
d) Given that Dealership B sold half as many trucks as Dealership A, we can substitute the value of "y" from Equation 1 into Equation 2 and solve for "x".
x + (225 - x) = 225
225 = 2x + (1/2)(225 - x)
450 = 4x + 225 - x/2
225 = 7x - x/2
450 = 14x - x
450 = 13x
x = 450/13
x ≈ 34.62
So, Dealership A sold approximately 34.62 trucks.
a) Let's represent the number of cars sold by Dealership A as 'C' and the number of trucks as 'T'. Since Dealership A sold a total of 225 cars and trucks, the equation for Dealership A would be:
C + T = 225
b) Let's represent the number of cars sold by Dealership B as 'C' and the number of trucks as 'T'. Dealership B sold twice as many cars as Dealership A and half as many trucks. Given that Dealership B sold a total of 300 cars and trucks, the equation for Dealership B would be:
2C + (1/2)T = 300
c) To find out how many cars Dealership A sold, we can use the equation from part (a). Rearrange the equation to solve for 'C':
C = 225 - T
Since we don't have the number of trucks sold for Dealership A, we cannot determine the exact number of cars sold by Dealership A.
d) Given that Dealership B sold half as many trucks as Dealership A, we can set up an equation to represent this relationship:
T = (1/2)T
In this equation, both sides are equal, meaning Trucks sold by Dealership A (T) is equal to half the number of trucks sold by Dealership B. However, this equation does not allow us to determine the actual number of trucks sold by either dealership.