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.
d) Given the fact that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?
Let's assume the number of trucks sold by Dealership A is T.
According to the given information, Dealership B sold half as many trucks as Dealership A, so the number of trucks sold by Dealership B is T/2.
We know that Dealership A sells a total of 225 cars and trucks, so we can write the equation:
T + (225 - T) = 225
Simplifying the equation, we have:
225 - T + T = 225
225 = 225
This equation is always true, which means the value of T doesn't matter. However, since we are asked to find the number of trucks sold by Dealership B, we don't need to find the value of T.
Therefore, we can conclude that Dealership B sold T/2 trucks.
To find out how many trucks Dealership B sold, we need to first determine how many trucks Dealership A sold.
We know that Dealership A sold a total of 225 cars and trucks. To find out how many trucks that is, we need to subtract the number of cars sold from the total.
If we let "x" represent the number of trucks sold by Dealership A, then the equation would be:
225 = x + number of cars sold by Dealership A
However, we don't know the exact number of cars sold by Dealership A yet. To figure that out, we can use the information given about the relationship between Dealership A and Dealership B's car sales.
The question states that Dealership B sold twice as many cars as Dealership A. If we let "y" represent the number of cars sold by Dealership A, then the equation would be:
number of cars sold by Dealership B = 2y
We also know from the question that Dealership B sold a total of 300 cars and trucks. So we can create another equation:
300 = number of trucks sold by Dealership B + number of cars sold by Dealership B
Since Dealership B sold half as many trucks as Dealership A, we can substitute the "x" and "y" values into our equations. We can also use the given information that Dealership B sold twice as many cars as Dealership A:
225 = x + y
300 = (x/2) + 2y
We now have a system of equations that we can solve to find the values of "x" and "y". Once we find the value of "x", we will have the answer to the question, which is the number of trucks sold by Dealership B.
Let's call the number of cars sold by Dealership A as "C" and the number of trucks sold as "T".
From the problem, we know that:
C + T = 225 [Equation 1]
We also know that Dealership B sold twice as many cars as Dealership A and half as many trucks. We can represent these as:
C = 2C [twice as many cars as Dealership A]
T = (1/2)T [half as many trucks as Dealership A]
Dealership B sold a total of 300 cars and trucks, so:
C + T = 300 [Equation 2]
Now we can substitute the values of C and T from Equation 1 into Equation 2:
225 = 300
225 - C = 300 - C
225 - C + C = 300 - C + C
225 = 300
Therefore, the number of trucks sold by Dealership B is 75.