A company owns two dealerships, both of which sell cars and ttrucks. Dealership A sells a toal 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.
a) An equation for the total cars and trucks for Dealership A:
b) An equation for the total cars and trucks for dealership B:
c) How many cars did Dealership A sell?:
d)Considering that Dealership B sold half as many trucks as dealership A, how many trucks did Dealership B sell?:
a) Let's represent the number of cars sold by Dealership A as C and the number of trucks as T. The equation for the total cars and trucks for Dealership A is C + T = 164.
b) Let's represent the number of cars sold by Dealership B as C' and the number of trucks as T'. The equation for the total cars and trucks for Dealership B is C' + T' = 229.
c) Since Dealership A sold a total of 164 cars and trucks, we can use equation (a) to determine the number of cars sold by Dealership A, which is C = 164 - T.
d) Considering that Dealership B sold half as many trucks as Dealership A, we can express the number of trucks sold by Dealership B as T' = 0.5T.
a) Let's represent the number of cars sold by Dealership A as "C_A" and the number of trucks sold as "T_A". Since Dealership A sells a total of 164 cars and trucks, we can write the equation as:
C_A + T_A = 164
b) For Dealership B, we know that it sells twice as many cars as Dealership A and half as many trucks. Let's represent the number of cars sold by Dealership B as "C_B" and the number of trucks sold as "T_B". We can write the equation as:
C_B + T_B = 229
c) To find the number of cars sold by Dealership A, we can substitute the value of "T_A" as 164 - C_A into the equation from part a:
C_A + (164 - C_A) = 164
164 - C_A = 164 - C_A
0 = 0
This equation does not give us any meaningful information. We can conclude that there is not enough information provided to determine the number of cars sold by Dealership A.
d) We are told that Dealership B sells half as many trucks as Dealership A. Since we do not have the exact number of trucks sold by Dealership A, we cannot determine the exact number of trucks sold by Dealership B.
a) The equation for the total cars and trucks sold by Dealership A can be represented as:
Cars + Trucks = 164
b) The equation for the total cars and trucks sold by Dealership B can be represented as:
Cars + Trucks = 229
c) To find how many cars Dealership A sold, we substitute the equation from part (a) into the equation from part (c), and solve for Cars:
Cars + Trucks = 164
Cars + (Cars/2) = 164
(3/2)Cars = 164
Cars = (2/3) * 164
Cars = 109.33
So, Dealership A sold approximately 109 cars.
d) Considering that Dealership B sold half as many trucks as Dealership A, we can write the equation as:
Trucks = (1/2) * Trucks (from Dealership A)
Substituting this equation into the equation from part (b), we can solve for Trucks:
Cars + Trucks = 229
Cars + (1/2) * Trucks (from Dealership A) = 229
Cars + (1/2) * Trucks = 229
Cars = 109 (as calculated in part c)
Substituting the value of Cars, we can solve for Trucks:
109 + (1/2) * Trucks = 229
(1/2) * Trucks = 229 - 109
(1/2) * Trucks = 120
Trucks = 240
So, Dealership B sold 240 trucks.