A company owns two dealerships, both of which sell cars and trucks. The first dealership sells a total of 164 cars and trucks. The second dealership sells twice as many cars and half as many trucks as the first dealership, and sells a total of 229 cars and trucks.
An equation for the total cars and trucks for dealership A:
x + y = 164
An equation for the total cars and trucks for dealership B:
1/2x + 1/2y = 229
How many cars did dealership A sell?
How many trucks did the dealership B sell?
We can use the information given in the problem to set up a system of two equations with two variables, which we can then solve to find the values of x and y.
The first equation we're given is x + y = 164, where x represents the number of cars sold by dealership A and y represents the number of trucks sold by dealership A.
The second equation we're given is 1/2x + 1/2y = 229, where 1/2x represents the number of cars sold by dealership B and 1/2y represents the number of trucks sold by dealership B.
We can simplify the second equation by multiplying both sides by 2, which gives us x + y = 458.
Now we have two equations that both represent the total number of cars and trucks sold by the two dealerships:
x + y = 164
x + y = 458
These equations contradict each other, since they imply that both x + y = 164 and x + y = 458, which is impossible. This means that there's no solution that satisfies both equations, and we'll have to go back and check whether we've correctly interpreted the problem.
One possible mistake we could have made is in assuming that dealership B sells both cars and trucks, when in fact it might only sell cars, or only sell trucks. If dealership B only sells cars, then the equation we were given would be x + 2y = 164 for dealership A and x = 229 for dealership B, since half of 229 is not a whole number. If dealership B only sells trucks, then the equation we were given would be 2x + y = 164 for dealership A and y = 229 for dealership B, since half of 164 is not a whole number.
Without more information from the problem, we can't be sure which scenario is correct, and so we can't give a definitive answer to how many cars dealership A sold or how many trucks dealership B sold.