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 the Dealership A, and sells a total of 300 cars and trucks. (4 points)
1.) How many cars did Dealership A sell?
2.) Given the fact that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?
1.) Dealership A sold 225 cars.
2.) Dealership B sold half as many trucks as Dealership A, so it sold 225/2 = <<225/2=112.5>>112.5 trucks. Since you can't sell half a truck, Dealership B sold 112 trucks.
1.) To find out how many cars Dealership A sold, we can use the information given that Dealership A sold a total of 225 cars and trucks.
To find the answers to these questions, we can follow a logical step-by-step approach. Let's break it down:
1. How many cars did Dealership A sell?
Since we are given that Dealership A sells a total of 225 cars and trucks, we need to determine the specific number of cars sold. We are not given how many trucks were sold, but we do know that the total number of cars and trucks sold was 225. Therefore, to find the number of cars sold, we need to subtract the number of trucks sold from the total.
Let's assume the number of trucks sold by Dealership A is T. So, the equation becomes:
Cars sold + Trucks sold = Total cars and trucks sold
Cars sold + T = 225
Now, let's move on to the second question.
2. Given the fact that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?
We already determined that Dealership A sold T trucks. According to the information given, Dealership B sold half as many trucks as Dealership A. Therefore, Dealership B sold T/2 trucks.
Now, let's use the information given to solve the equations:
Dealership A: Cars sold + T = 225
Dealership B: Cars sold + T/2 = 300
We need to solve these two equations simultaneously to find the values of Cars sold and T (the number of trucks sold by Dealership A).
To do this, we'll solve these equations in the following steps:
1. Isolate Cars sold in both equations:
Dealership A: Cars sold = 225 - T
Dealership B: Cars sold = 300 - (T/2)
2. Equate the two expressions for Cars sold:
225 - T = 300 - (T/2)
3. Solve for T:
Multiply every term by 2 to clear the fraction:
450 - 2T = 600 - T
Combine like terms:
-T + 2T = 600 - 450
T = 150
4. Substitute the value of T back into any of the original equations to find Cars sold by Dealership A:
Cars sold = 225 - T = 225 - 150 = 75
Therefore, the answers are:
1.) Dealership A sold 75 cars.
2.) Dealership B sold half as many trucks as Dealership A, so Dealership B sold 150/2 = 75 trucks.
But, Dealership A sold cars AND trucks, an their total was 225.
What was the amount of CARS the sold?
I apologize for the confusion. To find the number of cars sold by Dealership A, we need to subtract the number of trucks sold from the total of 225 cars and trucks.
Let's assume the number of trucks sold by Dealership A is T. So, the equation becomes:
Cars sold + Trucks sold = Total cars and trucks sold
Cars sold + T = 225
Since we want to find the number of cars sold, let's express Trucks sold in terms of Cars sold. We know that the dealership sold cars and trucks, but we don't have specific numbers for each category. Let's use C to represent the number of cars sold by Dealership A. Given that Dealership A sold a total of 225 cars and trucks, we can express the number of trucks sold as 225 - C.
Now we can write the equation as:
C + (225 - C) = 225
Simplifying the equation, we have:
225 = 225
This equation is true for any value of C. So, in this case, the number of cars sold by Dealership A could be any value. The question does not provide enough information to determine the specific number of cars sold by Dealership A.
The options for question 1.) is:
196, 132, 98, 125.
The options for Question 2.) is:
98, 50, 33, 59.
To find the number of cars sold by Dealership A, we need to subtract the number of trucks sold from the total of 225 cars and trucks.
Let's assume the number of trucks sold by Dealership A is T. So, the equation becomes:
Cars sold + Trucks sold = Total cars and trucks sold
Cars sold + T = 225
Given the options for question 1: 196, 132, 98, 125, we can test each option by substituting it into the equation and checking if the equation is true.
1.) Testing 196:
Cars sold + T = 225
196 + T = 225
T = 29
This does not satisfy the equation since the number of trucks cannot be 29 when the total is 225.
2.) Testing 132:
Cars sold + T = 225
132 + T = 225
T = 93
This does not satisfy the equation, as it would mean Dealership A sold more trucks than cars.
3.) Testing 98:
Cars sold + T = 225
98 + T = 225
T = 127
This does not satisfy the equation, as it would mean Dealership A sold more trucks than the total of 225.
4.) Testing 125:
Cars sold + T = 225
125 + T = 225
T = 100
This satisfies the equation since the sum of 125 cars and 100 trucks equals 225.
Therefore, the correct answer is:
1.) Dealership A sold 125 cars.
For question 2, we are given the fact that Dealership B sold half as many trucks as Dealership A. Using the previously determined value of 125 cars sold by Dealership A, we can calculate the number of trucks sold by Dealership B as half of the number of trucks sold by Dealership A.
125 / 2 = 62.5
Since Dealership B cannot sell half a truck, the closest option is 59.
Therefore, the correct answer is:
2.) Dealership B sold 59 trucks.
I'm sorry, but the last option for Question 2.) is 49, not 59.
Apologies for the mistake. Let's reevaluate the options for question 2:
Given the options for question 2: 98, 50, 33, 49, let's calculate the number of trucks sold by Dealership B using each option and see which one satisfies the given conditions.
1.) Testing 98:
Dealership B sold half as many trucks as Dealership A.
T(trucks sold by B) = T(trucks sold by A) / 2
T = 125 / 2
T = 62.5
This does not satisfy the condition since the number of trucks sold cannot be 62.5.
2.) Testing 50:
Dealership B sold half as many trucks as Dealership A.
T(trucks sold by B) = T(trucks sold by A) / 2
T = 125 / 2
T = 62.5
Again, this does not satisfy the condition since the number of trucks sold cannot be 62.5.
3.) Testing 33:
Dealership B sold half as many trucks as Dealership A.
T(trucks sold by B) = T(trucks sold by A) / 2
T = 125 / 2
T = 62.5
Once again, this does not satisfy the condition since the number of trucks sold cannot be 62.5.
4.) Testing 49:
Dealership B sold half as many trucks as Dealership A.
T(trucks sold by B) = T(trucks sold by A) / 2
T = 125 / 2
T = 62.5
This option does not satisfy the condition either since the number of trucks sold cannot be 62.5.
None of the given options satisfy the given condition of Dealership B selling half as many trucks as Dealership A. Please double-check the options provided for question 2.