A company owns two dealerships%2C 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%2C and sells a total of 229 cars and trucks. (4 points) a) An equation for the total cars and trucks for Dealership A%3A b) An equation for the total cars and trucks for Dealership B%3A c) How many cars did Dealership A sell%3F d) Considering that Dealership B sold half as many trucks as Dealership A%2C how many trucks did Dealership B sell%3F
a) Let's denote the number of cars Dealership A sells as "A_car" and the number of trucks it sells as "A_truck". Since the total number of cars and trucks sold by Dealership A is 164, we can write the equation: A_car + A_truck = 164.
b) Dealership B sells twice as many cars as Dealership A, so we can write the equation: B_car = 2*A_car. Dealership B sells half as many trucks as Dealership A, so we can write the equation: B_truck = 0.5*A_truck. The total number of cars and trucks sold by Dealership B is given as 229, so we can write the equation: B_car + B_truck = 229.
c) To find the number of cars Dealership A sold, we can substitute the value of B_car from equation (b) into equation (a): A_car + A_truck = 164. 2*A_car + 0.5*A_truck = 229. Solving these equations simultaneously, we find that A_car = 60.
d) Considering that Dealership B sold half as many trucks as Dealership A, we can substitute the value of A_truck from equation (a) into equation (b): B_car + B_truck = 229. B_car + 0.5*60 = 229. Solving this equation, we find that B_truck = 169.
a) Let's say "x" represents the number of cars sold by Dealership A and "y" represents the number of trucks sold by Dealership A. Since Dealership A sells a total of 164 cars and trucks, we can write the equation as follows:
x + y = 164
b) Let's say "a" represents the number of cars sold by Dealership B and "b" represents the number of trucks sold by Dealership B. We know that Dealership B sells twice as many cars as Dealership A and half as many trucks as Dealership A. Using this information, we can write the equation as follows:
a + b = 229
a = 2x
b = 0.5y
c) To find out how many cars Dealership A sold, we need to solve the equation from part a). By substituting the value of "y" from equation a) into equation b), we get:
x + (0.5y) = 229
x + (0.5 * 164) = 229
x + 82 = 229
x = 229 - 82
x = 147
Therefore, Dealership A sold 147 cars.
d) We already know that Dealership B sold half as many trucks as Dealership A, so b = 0.5y. By substituting the value of "y" from equation a) into equation b), we get:
a + (0.5y) = 229
a + (0.5 * 164) = 229
a + 82 = 229
a = 229 - 82
a = 147
Therefore, Dealership B sold 147 trucks.
a) Let's define the number of cars sold by Dealership A as 'C_A' and the number of trucks sold as 'T_A'. Since Dealership A sold a total of 164 cars and trucks, the equation for the total cars and trucks for Dealership A is:
C_A + T_A = 164
b) For Dealership B, it is mentioned that it sells twice as many cars and half as many trucks as Dealership A. So, let's define the number of cars sold by Dealership B as 'C_B' and the number of trucks sold as 'T_B'. The equation for the total cars and trucks for Dealership B is:
C_B + T_B = 229
c) To find out how many cars Dealership A sold, we need to use the information given in the equations. Since the total number of cars and trucks sold by Dealership A is 164, the equation becomes:
C_A + T_A = 164
But we want to find the number of cars sold, so we can isolate C_A:
C_A = 164 - T_A
Therefore, to determine the number of cars Dealership A sold, we need to know the number of trucks sold (T_A). Unfortunately, the exact number of trucks sold by Dealership A is not provided, making it impossible to determine the number of cars sold by Dealership A.
d) Similarly, to find out how many trucks Dealership B sold, we need to use the information given in the equations. It is mentioned that Dealership B sold half as many trucks as Dealership A. So, we can write the relation between the number of trucks sold by Dealership A (T_A) and the number of trucks sold by Dealership B (T_B) as:
T_B = 0.5 * T_A
Unfortunately, the exact number of trucks sold by Dealership A is not provided, making it impossible to determine the number of trucks sold by Dealership B.