A company owns two dealerships, both of which sell cars and trucks. The first dealership sells a total of 164 cars and trucks. The second dealership sells twice as many cars and half as many trucks as the first dealership, and sells a total of 229 cars and trucks.

Question

A company owns two dealerships, both of which sell cars and trucks. The first dealership sells a total of 164 cars and trucks. The second dealership sells twice as many cars and half as many trucks as the first dealership, and sells a total of 229 cars and trucks.

An equation for the total cars and trucks for dealership A:

An equation for the total cars and trucks for dealership B:

How many cars did dealership A sell?

How many trucks did the dealership B sell

Answer 1

Equations:

A = number of cars and trucks sold at dealership A
B = number of cars and trucks sold at dealership B
C = number of cars sold at dealership A

A = 164
B = (2C) + (0.5(164-C)) = 229

Simplifying the second equation:

B = 2C + 82

We can now solve for C by substituting the value of C into the second equation:

B = 2(73) + 82 = 228

Therefore, dealership A sold 73 cars and 91 trucks (164 - 73 = 91).

Dealership B sold 73 cars and 155 trucks (229 - 73 = 156, but we need to divide by 2 because they sold half as many trucks as dealership A, so 156/2 = 78, and 229 - 78 = 155).

Answer 2

Let's solve this step-by-step:

Step 1: Assign variables
Let's use the variables C_A and T_A to represent the number of cars and trucks sold by dealership A, and variables C_B and T_B to represent the number of cars and trucks sold by dealership B.

Step 2: Write equations
We are given the information that dealership A sells a total of 164 cars and trucks, so the equation is:
C_A + T_A = 164 --------(Equation 1)

Dealership B sells twice as many cars and half as many trucks as dealership A, and sells a total of 229 cars and trucks. So the equation for dealership B is:
C_B + T_B = 229 --------(Equation 2)

Step 3: Find values
From Equation 2, we can write:
C_B = 2C_A --------(Equation 3)
T_B = (1/2)T_A --------(Equation 4)

Step 4: Substitute values
Substituting Equations 3 and 4 into Equation 2, we get:
2C_A + (1/2)T_A = 229

Step 5: Simplify and solve
Multiplying the entire equation by 2 to eliminate the fraction, we have:
4C_A + T_A = 458

Step 6: Solve for variables
Now we have a system of equations:
C_A + T_A = 164
4C_A + T_A = 458

Subtracting Equation 1 from Equation 2, we find:
4C_A + T_A - (C_A + T_A) = 458 - 164
3C_A = 294

Dividing both sides by 3, we get:
C_A = 98

Since dealership A sells cars and trucks, we can substitute the value of C_A into Equation 1 to find the number of trucks:
98 + T_A = 164
T_A = 66

So, dealership A sold 98 cars and 66 trucks.

Dealership B sells twice as many cars as dealership A, so substituting C_A = 98 into Equation 3, we have:
C_B = 2(98)
C_B = 196

Dealership B sells half as many trucks as dealership A, so substituting T_A = 66 into Equation 4, we have:
T_B = (1/2)(66)
T_B = 33

Therefore, dealership B sold 196 cars and 33 trucks.

Answer 3

To find the equations for the total cars and trucks sold at each dealership, we need to assign variables to the number of cars and trucks sold by each dealership.

Let's assume:
- Let "C_A" represent the number of cars sold by dealership A.
- Let "T_A" represent the number of trucks sold by dealership A.
- Let "C_B" represent the number of cars sold by dealership B.
- Let "T_B" represent the number of trucks sold by dealership B.

Now, let's find the equations:

1. Equation for the total cars and trucks for dealership A:
C_A + T_A = 164

2. Equation for the total cars and trucks for dealership B:
C_B + T_B = 229

The question asks how many cars dealership A sold, so we need to solve for C_A.

We know that dealership B sells twice as many cars as dealership A, so we can write an additional equation:
C_B = 2*C_A

To find the value of C_A, we can substitute the value of C_B from equation 2 into equation 3, then substitute the value of C_A from equation 4 into equation 1 and solve:

C_A + T_A = 164 (equation 1)
(2*C_A) + T_B = 229 (equation 2)
C_B = 2*C_A (equation 3)

Substituting C_B from equation 3 into equation 2:
(2*C_A) + T_B = 229
2*C_A + T_B = 229 (equation 5)

Substituting the value of C_A from equation 4 into equation 1:
C_A + T_A = 164
(2*C_A) + T_A = 164 (equation 6)

Now, we have two equations with two variables: equation 5 and equation 6.
By solving these equations simultaneously, we can find the values of C_A and T_B.

After solving the equations, we can determine the number of cars dealership A sold (C_A) and the number of trucks dealership B sold (T_B).