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.
Given the fact that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?
Let's say Dealership A sold x cars and y trucks.
From the information given, x + y = 225.
Dealership B sold twice as many cars as Dealership A, which means it sold 2x cars.
It also sold half as many trucks as Dealership A, which means it sold 0.5y trucks.
The total number of cars and trucks sold by Dealership B is 2x + 0.5y = 300.
Since Dealership B sold half as many trucks as Dealership A, 0.5y = y/2.
Substituting the value of y from the first equation, we get 0.5(225-x) = (225-x)/2.
Multiplying through the parentheses, we get 112.5 - 0.5x = 112.5 - 0.5x.
Adding 0.5x to both sides, we get 0.5x = 112.5.
Dividing both sides by 0.5, we get x = 225.
Substituting the value of x into the equation 2x + 0.5y = 300, we get 2(225) + 0.5y = 300.
Simplifying, we get 450 + 0.5y = 300.
Subtracting 450 from both sides, we get 0.5y = -150.
Dividing both sides by 0.5, we get y = -300.
Therefore, Dealership B sold -300 trucks.
are you sure
Apologies for the incorrect answer.
Let's correct the solution:
Let's say Dealership A sold x cars and y trucks.
From the information given, x + y = 225.
Dealership B sold twice as many cars as Dealership A, which means it sold 2x cars.
It also sold half as many trucks as Dealership A, which means it sold 0.5y trucks.
The total number of cars and trucks sold by Dealership B is 2x + 0.5y = 300.
Since Dealership B sold half as many trucks as Dealership A, 0.5y = 0.5 * y = y/2.
Substituting the value of y from the first equation, we get 0.5(225-x) = (225-x)/2.
Multiplying through the parentheses, we get 112.5 - 0.5x = 112.5 - 0.5x.
Adding 0.5x to both sides, we get 0.5x = 112.5.
Dividing both sides by 0.5, we get x = 225.
Substituting the value of x into the equation 2x + 0.5y = 300, we get 2(225) + 0.5y = 300.
Simplifying, we get 450 + 0.5y = 300.
Subtracting 450 from both sides, we get 0.5y = -150.
Dividing both sides by 0.5, we get y = -300.
I apologize for the confusion, but these values do not make sense in this context. It seems there might be an error or missing information in the given problem statement.
Let's break down the information provided:
Dealership A sold a total of 225 cars and trucks.
Dealership B sold twice as many cars and half as many trucks as Dealership A, and a total of 300 cars and trucks.
To find out the number of trucks Dealership B sold, we need to find out how many cars and trucks Dealership A sold and then use that information to determine the number of trucks Dealership B sold.
From the given information, let's first determine the number of cars and trucks Dealership A sold. We know that Dealership A sold a total of 225 cars and trucks.
Let's assume the number of cars sold by Dealership A is x, and the number of trucks sold is y.
Therefore, we can set up a system of equations:
x + y = 225 ... (equation 1)
According to the given information, Dealership B sold twice as many cars and half as many trucks as Dealership A, which can be expressed as:
2x + (1/2)y = 300 ... (equation 2)
Now, let's solve this system of equations to find the values of x and y.
Multiplying equation 1 by 2, we get:
2x + 2y = 450
Subtracting equation 2 from this equation, we get:
2x + 2y - 2x - (1/2)y = 450 - 300
(3/2)y = 150
Dividing both sides of the equation by (3/2) gives us:
y = 150 * (2/3)
y = 100
Therefore, Dealership B sold 100 trucks.
To solve this question, let's break down the information given step by step:
1. Dealership A sells a total of 225 cars and trucks.
2. Dealership B sells twice as many cars and half as many trucks as Dealership A and sells a total of 300 cars and trucks.
Now, let's calculate the number of cars and trucks sold by Dealership B:
1. Let's assume that the number of cars sold by Dealership A is C1, and the number of trucks sold is T1.
2. From the information given, we know that Dealership B sold twice as many cars as Dealership A, so the number of cars sold by Dealership B is 2 * C1.
3. We also know that Dealership B sold half as many trucks as Dealership A, so the number of trucks sold by Dealership B is 0.5 * T1.
4. We also know that Dealership A sold a total of 225 cars and trucks, so we can write an equation: C1 + T1 = 225.
5. According to the information given, we also know that Dealership B sold a total of 300 cars and trucks, so we can write another equation: 2 * C1 + 0.5 * T1 = 300.
Now, we have a system of two equations with two variables (C1 and T1). We can solve these equations simultaneously to find the values of C1 and T1, which will give us the answer to how many trucks Dealership B sold.
By solving the equations, we get the value of C1 = 150 cars and T1 = 75 trucks.
Therefore, Dealership B sold 0.5 * T1 = 0.5 * 75 = 37.5 trucks. Since we can't have half a truck, we can round down to the nearest whole number.
Hence, Dealership B sold 37 trucks.