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 Dealership A, and sells a total of 300 cars and trucks.
1) How many CARS did Dealership A sell?
2) Considering that Dealership B sold half as many trucks as Dealership A, how many TRUCKS did Dealership B sell?
Let's solve the problem step by step.
1) We know that Dealership A sells a total of 225 cars and trucks. Let's assume that it sells x cars and y trucks. We can set up the equation: x + y = 225.
2) We also know that Dealership B sells twice as many cars and half as many trucks as Dealership A. This means that Dealership B sells 2 times x cars and 0.5 times y trucks. We can set up the second equation: 2x + 0.5y = 300.
Now we have a system of equations:
x + y = 225
2x + 0.5y = 300
To solve this system, we can use the substitution method. Let's solve the first equation for x:
x = 225 - y
Now we substitute this expression for x in the second equation:
2 * (225 - y) + 0.5y = 300
450 - 2y + 0.5y = 300
450 - 300 = 2y - 0.5y
150 = 1.5y
y = 150 / 1.5
y = 100
Now we can substitute the value of y in the first equation to find x:
x + 100 = 225
x = 225 - 100
x = 125
Therefore, Dealership A sold 125 cars and Dealership B sold 100 trucks.
To find the number of cars sold by Dealership A, we can directly use the information given, which states that Dealership A sold a total of 225 cars and trucks.
1) Therefore, Dealership A sold 225 cars.
Now, let's calculate the number of trucks sold by Dealership A.
If Dealership B sold half as many trucks as Dealership A, it means that Dealership B sold 1/2 * (number of trucks sold by Dealership A).
2) We know that the total number of cars and trucks sold by Dealership B is 300. Since we already know the number of cars sold by Dealership A, we can calculate the number of trucks sold by Dealership B.
Total number of cars and trucks sold by Dealership B = Number of cars sold by Dealership B + Number of trucks sold by Dealership B
300 = Number of cars sold by Dealership B + 1/2 * (number of trucks sold by Dealership A)
To find the number of trucks sold by Dealership B, we rearrange the equation:
Number of trucks sold by Dealership B = 300 - Number of cars sold by Dealership B
Now, let's substitute the value we found in Step 1:
Number of trucks sold by Dealership B = 300 - 225
Number of trucks sold by Dealership B = 75
Therefore, Dealership B sold 75 trucks.
To find the number of cars sold by Dealership A (question 1), we can subtract the number of trucks sold by Dealership A from the total number of vehicles (225).
To find the number of trucks sold by Dealership A, we need to determine the difference between the total number of vehicles sold by both dealerships (225 + 300) and the number of cars sold by Dealership B (question 2).
Then, using the information that Dealership B sold half as many trucks as Dealership A, we can divide the number of trucks sold by Dealership B by half to get the number of trucks sold by Dealership A.
Let's calculate:
1) Number of cars sold by Dealership A:
Total vehicles sold by Dealership A (225) - Number of trucks sold by Dealership A
2) Number of trucks sold by Dealership B:
Total vehicles sold by both dealerships (225 + 300) - Number of cars sold by Dealership B
Number of trucks sold by Dealership A = (Number of trucks sold by Dealership B) / 2
Now, let's compute the answers:
1) Number of cars sold by Dealership A:
225 - [Total vehicles sold by both dealerships (225 + 300) - Number of cars sold by Dealership B]
2) Number of trucks sold by Dealership B:
[Total vehicles sold by both dealerships (225 + 300) - Number of cars sold by Dealership B] / 2
Once we determine the value of the expressions above, we can answer questions 1 and 2 accordingly.