c) To find the number of cars Dealership A sold, we can set up the equation x + y = 225, where x represents the number of cars and y represents the number of trucks. Since we want to find the number of cars, we need to solve for x. Rearranging the equation, we have x = 225 - y.
d) Given that Dealership B sold half as many trucks as Dealership A, we can express this relationship as y = 1/2x.
To calculate the values of x and y, we can substitute the second equation into the first equation and solve for x.
(1) x + y = 225
(2) x = 225 - y (substitute y = 1/2x from the second equation into the first equation)
Now, substitute equation (2) into equation (1):
(225 - y) + y = 225
225 - y + y = 225
225 = 225
This equation is true for any value of y. Therefore, there are infinitely many solutions for x and y, meaning we cannot determine the exact number of cars Dealership A sold.
To find the number of trucks Dealership B sold, we can substitute the expression for x from the second equation into the second equation:
2(225 - y) + 1/2y = 300
450 - 2y + 1/2y = 300
450 - 2y/1 + 1/2y = 300
450 - 4y + y = 600
450 + 3y = 600
3y = 150
y = 50
Dealership B sold 50 trucks.
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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:
x + y = 225
b) An equation for the total cars and trucks for Dealership B:
2x + 1/2y = 300
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?
1 answer
3 answers