A company owns two dealerships, both of which sells cars and trucks. Dealerships A sell a total 164, cars and trucks. Dealerships B sells twice as many car and half as many trucks as dealerships A, and sells a total of 229 cars and trucks
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 information given, Dealership A sells a total of 164 cars and trucks, so we can write the equation:
c + t = 164 ----(1)
Dealership B sells twice as many cars as Dealership A, so the number of cars sold by Dealership B is 2c. Dealership B sells half as many trucks as Dealership A, so the number of trucks sold by Dealership B is (1/2)t. The total number of cars and trucks sold by Dealership B is given as 229, so we can write the equation:
2c + (1/2)t = 229 ----(2)
Now, we can solve these two equations simultaneously to find the values of c and t.
From equation (1), we can express c in terms of t:
c = 164 - t
Substituting this value of c into equation (2):
2(164 - t) + (1/2)t = 229
328 - 2t + (1/2)t = 229
328 - 229 = (3/2)t
99 = (3/2)t
Multiplying both sides by 2/3:
t = (2/3) * 99
t = 66
Substituting this value of t into equation (1):
c + 66 = 164
c = 164 - 66
c = 98
Therefore, Dealership A sells 98 cars and 66 trucks, while Dealership B sells 2 * 98 = 196 cars and (1/2) * 66 = 33 trucks.
To solve this problem, we can use a system of equations. Let's denote the number of cars sold by dealership A as 'CarsA', the number of trucks sold by dealership A as 'TrucksA', the number of cars sold by dealership B as 'CarsB', and the number of trucks sold by dealership B as 'TrucksB'.
According to the given information, we can set up the following equations:
Equation 1: CarsA + TrucksA = 164
Equation 2: CarsB + TrucksB = 229
We also know that dealership B sells twice as many cars as dealership A and half as many trucks as dealership A. Therefore, we can write the following equations:
Equation 3: CarsB = 2 * CarsA
Equation 4: TrucksB = 0.5 * TrucksA
Now, let's solve this system of equations to find the values of CarsA, TrucksA, CarsB, and TrucksB.
From Equation 3, we can express CarsA in terms of CarsB: CarsA = CarsB / 2
Substitute this into Equation 1 to get:
(CarsB / 2) + TrucksA = 164
Multiply both sides of the equation by 2 to eliminate the fraction:
CarsB + 2 * TrucksA = 328
Let's rewrite Equation 2 in terms of TrucksA using Equation 4:
CarsB + 0.5 * TrucksA = 229
Now we have a system of two equations with two unknowns:
CarsB + 2 * TrucksA = 328 (Equation 5)
CarsB + 0.5 * TrucksA = 229 (Equation 6)
Next, we can subtract Equation 6 from Equation 5 to eliminate CarsB:
(CarsB + 2 * TrucksA) - (CarsB + 0.5 * TrucksA) = 328 - 229
1.5 * TrucksA = 99
Divide both sides of the equation by 1.5:
TrucksA = 99 / 1.5 = 66
Now, substitute this value back into Equation 1 to find the value of CarsA:
CarsA + TrucksA = 164
CarsA + 66 = 164
CarsA = 164 - 66 = 98
Since dealership B sells twice as many cars as dealership A, we can find the value of CarsB:
CarsB = 2 * CarsA = 2 * 98 = 196
Lastly, substitute the values of TrucksA and CarsB into Equation 6 to find the value of TrucksB:
CarsB + 0.5 * TrucksA = 229
196 + 0.5 * 66 = 229
196 + 33 = 229
TrucksB = 33
Therefore, dealership A has sold 98 cars and 66 trucks, while dealership B has sold 196 cars and 33 trucks.
To solve this problem step-by-step, let's break it down into smaller parts.
Step 1: Define variables
Let's assign variables to represent the number of cars and trucks in Dealership A.
Let's call the number of cars in Dealership A as "CA" and the number of trucks as "TA".
Step 2: Find the total number of cars and trucks in Dealership A
From the information given, Dealership A sells a total of 164 cars and trucks.
So, CA + TA = 164.
Step 3: Define variables for Dealership B
Let's assign variables for Dealership B as well.
The number of cars in Dealership B is twice as many as Dealership A, so it can be represented as 2CA.
The number of trucks in Dealership B is half as many as Dealership A, so it can be represented as 0.5TA.
Step 4: Find the total number of cars and trucks in Dealership B
From the information given, Dealership B sells a total of 229 cars and trucks.
So, 2CA + 0.5TA = 229.
Step 5: Solve the two equations
We have two equations:
CA + TA = 164 (Equation 1)
2CA + 0.5TA = 229 (Equation 2)
Step 6: Solve the equations
We can use substitution or elimination method to solve the equations. Let's use the elimination method.
Multiply Equation 1 by 2 to make the coefficients of CA equal:
2(CA + TA) = 2(164)
2CA + 2TA = 328 (Equation 3)
Now we can subtract Equation 3 from Equation 2:
(2CA + 0.5TA) - (2CA + 2TA) = 229 - 328
-1.5TA = -99
Divide both sides by -1.5 to solve for TA:
TA = -99 / -1.5
TA = 66
Step 7: Substitute the value of TA into Equation 1 to solve for CA:
CA + 66 = 164
CA = 164 - 66
CA = 98
Step 8: Calculate the number of cars and trucks in Dealership B
The number of cars in Dealership B is 2CA = 2 * 98 = 196.
The number of trucks in Dealership B is 0.5TA = 0.5 * 66 = 33.
Final Answer:
Dealership A sells 98 cars and 66 trucks.
Dealership B sells 196 cars and 33 trucks.