a) An equation for the total cars and trucks for Dealership A:
Let x be the number of cars sold by Dealership A and y be the number of trucks sold by Dealership A.
The total cars and trucks sold by Dealership A can be represented by the equation: x + y = 225.
b) An equation for the total cars and trucks for Dealership B:
Dealership B sells twice as many cars as Dealership A, so the number of cars sold by Dealership B is 2x.
Dealership B sells half as many trucks as Dealership A, so the number of trucks sold by Dealership B is (1/2)y.
The total cars and trucks sold by Dealership B can be represented by the equation: 2x + (1/2)y = 300.
c) To find the number of cars sold by Dealership A, we can substitute the value of y from equation a) into equation b) and solve for x:
2x + (1/2)y = 300
2x + (1/2)(225 - x) = 300
2x + 112.5 - (1/2)x = 300
(3/2)x + 112.5 = 300
(3/2)x = 300 - 112.5
(3/2)x = 187.5
x = (2/3) * 187.5
x ≈ 125
Dealership A sold approximately 125 cars.
d) Given that Dealership B sold half as many trucks as Dealership A, we can substitute the value of x from part c) into equation a) and solve for y:
x + y = 225
125 + y = 225
y = 225 - 125
y = 100
Dealership B sold 100 trucks.
Use your graphing calculator: Desmos Graphing Calculator 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? d) Given the fact that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?
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