A company owns two dealerships, both of which sell cars and trucks. Dealership A sells a total of 164 cars and trucks. Dealership B sells twice as many cars and half as many trucks as Dealership A, and sells a total of 229 cars and trucks. (4 points) a) c) How many cars did Dealership A sell?

Answer 1

Let's say the number of cars sold by Dealership A is x.
Dealership B sells twice as many cars as Dealership A, meaning it sold 2x cars.
Dealership A also sells trucks, which we'll represent as y.
Dealership B sells half as many trucks as Dealership A, meaning it sold 0.5y trucks.
The total number of cars and trucks sold by Dealership A is x + y = 164.
The total number of cars and trucks sold by Dealership B is 2x + 0.5y = 229.
From these two equations, we can create a system of equations:
x + y = 164
2x + 0.5y = 229
We can solve this system of equations. Let's multiply the first equation by 2 to eliminate the y variable:
2(x + y) = 2(164)
2x + 2y = 328
Now let's subtract the second equation from this result:
(2x + 2y) - (2x + 0.5y) = 328 - 229
2x + 2y - 2x - 0.5y = 99
1.5y = 99
Now we can isolate the y variable by dividing both sides by 1.5:
y = 99 / 1.5 = 66
Now we can substitute this value back into the first equation to solve for x:
x + 66 = 164
x = 164 - 66 = 98
Therefore, Dealership A sold 98 cars. Answer: \boxed{98}.