A company owns two dealerships, both of which sell cars and trucks. Dealership A sells a total of 164 cars and trucks. Dealership B sells twice as many cars and half as many trucks as Dealership A, and sells a total of 229 cars and trucks.
How many cars did Dealership A sell?
Considering 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, we can create two equations.
The first equation states that dealership A sells a total of 164 cars and trucks: X + Y = 164.
The second equation states that dealership B sells twice as many cars and half as many trucks as dealership A, and sells a total of 229 cars and trucks.
Since dealership B sells half as many trucks as dealership A, the equation for the trucks will be Y/2.
So the second equation is: 2(X) + (Y/2) = 229.
Now we can solve this system of equations.
Multiply the first equation by 2 to eliminate Y:
2X + 2Y = 328.
Multiply the second equation by 2 to eliminate the denominator:
4X + Y = 458.
Now, subtract the first equation from the second equation:
(4X + Y) - (2X + 2Y) = 458 - 328.
2X - Y = 130.
Now, add this equation to the first equation:
(2X - Y) + (X + Y) = 130 + 164.
3X = 294.
Finally, divide both sides of the equation by 3 to solve for X:
X = 294 / 3.
X = 98.
Therefore, dealership A sold 98 cars.
To find the number of trucks dealership B sold, plug X = 98 into the second equation:
2(98) + (Y/2) = 229.
196 + (Y/2) = 229.
Y/2 = 229 - 196.
Y/2 = 33.
Multiply both sides of the equation by 2 to find Y:
Y = 2 * 33.
Y = 66.
Therefore, dealership B sold 66 trucks.
Let's solve this step-by-step.
Step 1:
Let's assume the number of cars sold by Dealership A is "C" and the number of trucks sold by Dealership A is "T".
Step 2:
According to the information provided, Dealership A sells a total of 164 cars and trucks.
C + T = 164
Step 3:
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 (1/2)T.
Step 4:
According to the information provided, Dealership B sells a total of 229 cars and trucks.
2C + (1/2)T = 229
Step 5:
We have two equations:
C + T = 164
2C + (1/2)T = 229
Step 6:
Let's solve these equations to find the values of C and T.
Multiplying equation 2 by 2 to eliminate fractions:
4C + T = 458
Step 7:
Subtracting equation 1 from equation 2:
4C + T - (C + T) = 458 - 164
3C = 294
Step 8:
Dividing both sides of the equation by 3:
C = 294 / 3
C = 98
Step 9:
Plugging the value of C into equation 1 to find the value of T:
98 + T = 164
T = 164 - 98
T = 66
Therefore, Dealership A sold 98 cars and 66 trucks.
Dealership B sold half as many trucks as Dealership A, so Dealership B sold 66/2 = 33 trucks.
To find out how many cars Dealership A sold, we need to use the information given. It states that Dealership B sells twice as many cars as Dealership A. Let's assume Dealership A sold X number of cars.
So, Dealership B sold twice as many cars as Dealership A, which means Dealership B sold 2X cars.
Now, let's look at the second part of the question. It says that Dealership A sells a total of 164 cars and trucks. We know that Dealership A sold X cars, but we don't know how many trucks they sold. Let's call the number of trucks Dealership A sold as Y.
So, the total number of cars and trucks sold by Dealership A is X + Y = 164.
Moving on to the second part of the question, it states that Dealership B sells half as many trucks as Dealership A. So, the number of trucks sold by Dealership B is 0.5Y.
Furthermore, the question also says that Dealership B sold a total of 229 cars and trucks. We know that Dealership B sold 2X cars and 0.5Y trucks.
Hence, the total number of cars and trucks sold by Dealership B is 2X + 0.5Y = 229.
Now we have a system of two equations:
X + Y = 164 (Equation 1)
2X + 0.5Y = 229 (Equation 2)
We can solve this system of equations to find the values of X and Y.