a company owns two dealerships both of which sell cars and trucks. Dealership A sells a total of 164 cars and trucks dearlership B sells twice as many cars and half as many trucks as Dealership A. and sells a total of 229 cars and trucks
How many cars did dealership A sell
Let's call the number of cars sold by Dealership A "x".
According to the problem, Dealership B sells twice as many cars as Dealership A, so the number of cars sold by Dealership B is 2x.
Dealership B also sells half as many trucks as Dealership A. If Dealership A sells "x" total cars and trucks, then it sells x - x/2 = x/2 trucks. Similarly, Dealership B sells (2x)/2 = x/2 trucks.
To find the total number of cars and trucks sold by Dealership A and Dealership B, we can add the number of cars and trucks sold separately.
Dealership A sells x cars and x/2 trucks, so the total number of cars and trucks sold by Dealership A is x + x/2 = 3x/2.
Dealership B sells 2x cars and x/2 trucks, so the total number of cars and trucks sold by Dealership B is 2x + x/2 = 5x/2.
According to the problem, the total number of cars and trucks sold by both dealerships is 229.
Therefore, we can set up the following equation:
3x/2 + 5x/2 = 229
Adding the fractions on the left side of the equation, we get:
8x/2 = 229
Simplifying the left side of the equation, we get:
4x = 229
Dividing both sides of the equation by 4, we get:
x = 57.25
Since we can't have a fractional number of cars sold, Dealership A sold 57 cars.
Let's assume the number of cars sold by Dealership A as 'x'. According to the given information, Dealership B sells twice as many cars as Dealership A, so the number of cars sold by Dealership B would be '2x'.
We are also told that Dealership A sold a total of 164 cars and trucks. Thus, the equation representing this information would be:
x + number of trucks sold by Dealership A = 164
Similarly, Dealership B sold a total of 229 cars and trucks, and the equation representing this information would be:
2x + number of trucks sold by Dealership B = 229
Since we are only interested in finding the number of cars sold by Dealership A, we need to eliminate the variable 'number of trucks.' From the first equation, we can rewrite it as:
number of trucks sold by Dealership A = 164 - x
Now, substituting this expression into the second equation, we have:
2x + (164 - x)/2 = 229
To solve this equation, we can first multiply the entire equation by 2 to remove the fraction:
4x + 164 - x = 458
Combining like terms, we get:
3x + 164 = 458
Subtracting 164 from both sides of the equation yields:
3x = 458 - 164
3x = 294
Finally, dividing both sides by 3, we find:
x = 294 / 3
x = 98
Therefore, Dealership A sold 98 cars.
To find out how many cars Dealership A sold, we can start by setting up a system of equations based on the given information.
Let's assume:
- The number of cars Dealership A sold = x
- The number of trucks Dealership A sold = y
From the problem, we know:
- Dealership A sold a total of 164 cars and trucks, so x + y = 164
- Dealership B sold twice as many cars as Dealership A, so Dealership B sold 2x cars
- Dealership B also sold half as many trucks as Dealership A, so Dealership B sold (1/2)y trucks
- Dealership B sold a total of 229 cars and trucks, so 2x + (1/2)y = 229
We can now solve this system of equations to find the value of x, which represents the number of cars Dealership A sold.
From the first equation, we can rewrite it as y = 164 - x.
Substitute this value of y in the second equation:
2x + (1/2)(164 - x) = 229
Simplify the equation:
2x + 82 - (1/2)x = 229
Multiply both sides of the equation by 2 to eliminate the fraction:
4x + 164 - x = 458
Combine like terms:
3x = 458 - 164
3x = 294
Divide both sides by 3:
x = 98
Therefore, Dealership A sold a total of 98 cars.