a) Let's assume the number of cars sold at Dealership A is c and the number of trucks sold at Dealership A is t. Therefore, the equation for the total cars and trucks for Dealership A is:
c + t = 225
b) Let's assume the number of cars sold at Dealership B is x and the number of trucks sold at Dealership B is y. We know that Dealership B sells twice as many cars as Dealership A and half as many trucks as Dealership A. Therefore, the equation for the total cars and trucks for Dealership B is:
x + y = 300
c) We can substitute the equation for Dealership A in equation b) to find the value of c:
x + y = 225 + t (Substituting c + t = 225)
From the given information that Dealership B sells twice as many cars as Dealership A, we can substitute x = 2c in the above equation:
2c + y = 225 + t
We also know that the total cars and trucks for Dealership B is 300, so we can rewrite the equation b) as:
(2c) + y = 300
Now, we have a system of equations:
2c + y = 300
2c + y = 225 + t
Since the coefficients of c in both equations are the same, we can subtract the second equation from the first equation to eliminate c:
2c + y - (2c + y) = 300 - (225 + t)
0 = 75 - t
t = 75
Therefore, Dealership A sold 75 trucks.
d) We can substitute the value of t = 75 in equation b) to find the value of y:
x + y = 225 + t (Substituting t = 75)
x + y = 225 + 75
x + y = 300
Since we are asked to find the number of trucks Dealership B sold, which is represented by y, we can conclude that Dealership B sold 75 trucks.
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 Dealership A, and sells a total of 300 cars and trucks.
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?
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