A company owns two dealerships, both of which sales cars and trucks dealership. I says a total of 225 cars and trucks dealership base sells twice as many cars and half as many trucks does the dealership a and sells a total of 300 cars and trucks how many cars at dealership a sale
Let's assume the number of cars sold at dealership A is x.
Since dealership B sells twice as many cars as dealership A, dealership B sells 2x cars.
The total number of cars sold at both dealerships is x + 2x = 3x.
Therefore, 3x = 225 (given), which means x = 225/3 = 75.
So, dealership A sells 75 cars.
To find out how many cars the dealership A sells, we can use the given information.
Let's assume the number of cars sold by dealership A is represented by 'x'.
According to the information given, the total number of cars and trucks sold by dealership A is 225. Therefore, we can write an equation:
x + (0.5x) = 225
Simplifying this equation, we have:
1.5x = 225
Dividing both sides of the equation by 1.5:
x = 225 / 1.5
x = 150
So, dealership A sells 150 cars.
Let's solve this step-by-step.
Step 1: Let's assume the number of cars sold at dealership A is "x".
Step 2: It is given that dealership B sells twice as many cars as dealership A, so the number of cars sold at dealership B is 2x.
Step 3: It is also given that dealership B sells half as many trucks as dealership A. Let's assume the number of trucks sold at dealership A is "y", so the number of trucks sold at dealership B is y/2.
Step 4: According to the information provided, the total number of cars and trucks sold at dealership A is 225. So, we can express this as an equation:
x + y = 225
Step 5: Similarly, the total number of cars and trucks sold at dealership B is 300. So, we can express this as another equation:
2x + (y/2) = 300
Step 6: Let's simplify equation 5 by multiplying every term by 2 to eliminate the fraction:
4x + y = 600
Step 7: Now we have a system of two equations with two variables:
Equation 1: x + y = 225
Equation 2: 4x + y = 600
Step 8: We can solve this system using any method like substitution or elimination. Let's solve it using the substitution method.
Step 9: Rearrange Equation 1 to express y in terms of x:
y = 225 - x
Step 10: Substitute the value of y in Equation 2 with the expression from step 9:
4x + (225 - x) = 600
Step 11: Simplify the equation:
3x + 225 = 600
3x = 600 - 225
3x = 375
Step 12: Solve for x by dividing both sides of the equation by 3:
x = 375/3
x = 125
Step 13: Now substitute the value of x in Equation 1 to find y:
125 + y = 225
y = 225 - 125
y = 100
Therefore, dealership A sells 125 cars.