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
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?
a) Let's suppose the number of cars sold by Dealership A is x and the number of trucks sold by Dealership A is y. The equation for the total cars and trucks sold by Dealership A can be written as x + y = 164.
b) Let's suppose the number of cars sold by Dealership B is 2x (twice as many cars as Dealership A) and the number of trucks sold by Dealership B is y/2 (half as many trucks as Dealership A). The equation for the total cars and trucks sold by Dealership B can be written as 2x + y/2 = 229.
c) From equation a), we know that x + y = 164. Since we only want to find the number of cars sold by Dealership A, we can rewrite this equation as x = 164 - y.
d) Since Dealership B sold half as many trucks as Dealership A, we know that y/2 is the number of trucks sold by Dealership B. From equation b), we have 2x + y/2 = 229. We can substitute x with 164 - y to get 2(164 - y) + y/2 = 229.
b) An equation for the total cars and trucks for Dealership B:
Let x be the number of cars and y be the number of trucks sold by Dealership A.
Since Dealership B sells twice as many cars as Dealership A and half as many trucks, the equation can be written as:
x = 2(x) (twice as many cars as Dealership A)
y = (1/2)(y) (half as many trucks as Dealership A)
229 = 2x + y
c) To find how many cars Dealership A sold, we use the equation given in part a:
164 = x + y
Solving these two equations simultaneously will give us the values of x and y, representing the number of cars and trucks sold by Dealership A.
d) To find how many trucks Dealership B sold, we use the equation given in part b:
y = (1/2)(y)
Substituting the value of y into the equation from part b, we can find the number of trucks sold by Dealership B.
To find the equations for the total cars and trucks for both dealerships, we need to represent the given information mathematically.
Let's assign:
x = number of cars sold by Dealership A
y = number of trucks sold by Dealership A
So, the equation for the total cars and trucks sold by Dealership A would be:
x + y = 164
According to the information, Dealership B sells twice as many cars and half as many trucks as Dealership A. Therefore, the equation for the total cars and trucks sold by Dealership B would be:
2x + (1/2)y = 229
Now, to find how many cars Dealership A sold, we can use the first equation. Rearrange it to solve for x:
x + y = 164
x = 164 - y
So, Dealership A sold 164 - y cars.
To determine how many trucks Dealership B sold, we need to consider that Dealership B sold half as many trucks as Dealership A. We know that Dealership A sold y trucks, so Dealership B sold (1/2)y trucks.
Now, let's substitute these values into the equation for the total cars and trucks sold by Dealership B:
2x + (1/2)y = 229
2(164 - y) + (1/2)y = 229
328 - 2y + (1/2)y = 229
(3/2)y = 328 - 229
(3/2)y = 99
y = (99 * 2) / 3
y = 66
Therefore, Dealership A sold 164 - 66 = 98 cars, and Dealership B sold 66 trucks.