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. %0D%0A%0D%0A(4 points)%0D%0Aa) An equation for the total cars and trucks for Dealership A: %0D%0A%0D%0Ab) An equation for the total cars and trucks for Dealership B: %0D%0A%0D%0Ac) How many cars did Dealership A sell? %0D%0A%0D%0Ad) Considering that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?
a) To find the equation for the total cars and trucks sold by Dealership A, we can let the number of cars sold be represented by 'C', and the number of trucks sold be represented by 'T'. The equation would be:
C + T = 164
b) To find the equation for the total cars and trucks sold by Dealership B, we know that it sells twice as many cars as Dealership A, so the number of cars sold by Dealership B would be 2C. Additionally, it sells half as many trucks as Dealership A, so the number of trucks sold by Dealership B would be (1/2)T. The equation would be:
2C + (1/2)T = 229
c) To find the number of cars Dealership A sold, we can substitute the equation from part a) into the equation from part b).
When we substitute C + T = 164 into 2C + (1/2)T = 229, we get:
2(164 - T) + (1/2)T = 229
Simplifying, we get:
328 - 2T + (1/2)T = 229
Combining like terms, we get:
(1/2)T = 101
Multiplying both sides by 2 to eliminate the fraction, we get:
T = 202
Therefore, Dealership A sold 202 trucks.
d) Considering that Dealership B sold half as many trucks as Dealership A, we can simply divide the number of trucks sold by Dealership A by 2 to find the number of trucks sold by Dealership B.
So, Dealership B sold 202 / 2 = 101 trucks.
a) Let's assume the number of cars sold by Dealership A is C1 and the number of trucks sold by Dealership A is T1. Therefore, the equation for the total cars and trucks sold by Dealership A can be written as:
C1 + T1 = 164
b) Let's assume the number of cars sold by Dealership B is C2 and the number of trucks sold by Dealership B is T2. According to the given information, Dealership B sells twice as many cars as Dealership A and half as many trucks as Dealership A. Therefore, the equation for the total cars and trucks sold by Dealership B can be written as:
C2 + T2 = 229
c) From the equation in part a), we know that C1 + T1 = 164. To find the number of cars sold by Dealership A, we need to isolate C1. This can be done by subtracting T1 from both sides of the equation:
C1 = 164 - T1
d) According to the given information, Dealership B sold half as many trucks as Dealership A. Therefore, T2 can be expressed as T1/2. We can substitute this value in the equation from part b) to find the number of trucks sold by Dealership B:
C2 + T1/2 = 229.
a) Let's represent the total cars and trucks sold by Dealership A as "x." Since we know that Dealership A sells a total of 164 cars and trucks, the equation would be:
x = 164
b) Similarly, let's represent the total cars and trucks sold by Dealership B as "y." Since we know that Dealership B sells twice as many cars and half as many trucks as Dealership A, the equation would be:
y = 2(164) + 0.5(164)
c) To find out how many cars Dealership A sold, we substitute the value of "x" from equation a) into this equation.
So, Dealership A sold:
x = 164 cars
d) We know that Dealership B sold half as many trucks as Dealership A, and since we already know the number of trucks sold by Dealership A, we can find the number of trucks sold by Dealership B by substituting the value of "x" from equation a) into this equation.
Thus, Dealership B sold:
Trucks = 0.5(164)
The answer will depend on the value you get when you calculate 0.5(164). Please calculate it.