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.
How many CARS did Dealership A sell?
To find out how many cars Dealership A sold, we need to solve the given problem. Let's break down the information we have:
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.
First, let's assume the number of cars sold by Dealership A is C, and the number of trucks sold is T. Therefore, we have two unknowns, C and T.
From the given information, we know:
C + T = 225 (Equation 1) - Dealership A's total sales
2C + 0.5T = 300 (Equation 2) - Dealership B's total sales
Now, we have a system of equations to solve simultaneously. We can solve this system using various methods, such as substitution or elimination. Let's use substitution:
From Equation 1, we can rearrange it to C = 225 - T.
Substitute this value of C into Equation 2:
2(225 - T) + 0.5T = 300
Simplify the equation:
450 - 2T + 0.5T = 300
-1.5T = -150
T = -150 / -1.5
T = 100
Substitute the value of T back into Equation 1:
C + 100 = 225
C = 225 - 100
C = 125
Therefore, Dealership A sold 125 cars.
Let's assume the number of cars sold by Dealership A is C, and the number of trucks sold by Dealership A is T.
According to the given information, the total number of cars and trucks sold by Dealership A is 225:
C + T = 225 ........(equation 1)
Now, let's analyze the information for Dealership B. It is mentioned that Dealership B sells twice as many cars as Dealership A and half as many trucks as Dealership A.
So, the number of cars sold by Dealership B is 2C.
And the number of trucks sold by Dealership B is T/2.
According to the given information, the total number of cars and trucks sold by Dealership B is 300:
2C + T/2 = 300 ........(equation 2)
We have two equations with two variables (C and T). We can solve these equations to find the values of C and T.
First, let's simplify equation 2 by multiplying both sides by 2:
2(2C) + 2(T/2) = 2(300)
4C + T = 600 ........(equation 3)
Now, we have two equations:
C + T = 225 ........(equation 1)
4C + T = 600 ........(equation 3)
To solve these equations, we can subtract equation 1 from equation 3:
(4C + T) - (C + T) = 600 - 225
3C = 375
Dividing both sides of the equation by 3, we get:
C = 375/3
C = 125
Therefore, Dealership A sold 125 cars.
are you sure??
Apologies for the confusion. Let's solve the equations again to find the correct answer.
The equations we have are:
C + T = 225 ........(equation 1)
2C + 0.5T = 300 .......(equation 2)
To make equation 2 simpler, let's multiply it by 2 to remove the decimal:
4C + T = 600 .......(equation 3)
Now, we can subtract equation 1 from equation 3:
(4C + T) - (C + T) = 600 - 225
3C = 375
C = 375/3
C = 125
Therefore, Dealership A sold 125 cars.
Given the fact that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?
If Dealership B sold half as many trucks as Dealership A, and Dealership A sold T trucks, then Dealership B sold T/2 trucks.
In this case, we have already found that Dealership A sold 125 cars (C = 125). To find the number of trucks sold by Dealership A, we can substitute this value into equation 1:
125 + T = 225
T = 225 - 125
T = 100
So, Dealership A sold 100 trucks.
Since Dealership B sold half as many trucks as Dealership A, Dealership B must have sold 100/2 = 50 trucks.