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) The equation for the total cars and trucks for Dealership A is:
C + T = 164
where C represents the number of cars and T represents the number of trucks.
b) The equation for the total cars and trucks for Dealership B is:
2C + (1/2)T = 229
where C represents the number of cars and T represents the number of trucks.
c) We can solve the equation C + T = 164 to find the number of cars Dealership A sold:
C + T = 164
C + T - T = 164 - T
C = 164 - T
d) Considering that Dealership B sold half as many trucks as Dealership A, we can substitute the value of T from equation c into equation b:
2C + (1/2)T = 229
2(164 - T) + (1/2)T = 229
328 - 2T + (1/2)T = 229
(1/2)T = 229 - 328 + 2T
(1/2)T = -99 + 2T
(1/2)T - 2T = -99
-3/2 T = -99
T = (-99)/(-3/2)
T = 66
Therefore, Dealership A sold 66 trucks.
a) Let's assume the number of cars sold by Dealership A is c and the number of trucks sold is t. The equation for the total cars and trucks sold by Dealership A can be written as:
c + t = 164
b) Let's assume the number of cars sold by Dealership B is C and the number of trucks sold is T. According to the given information, Dealership B sells twice as many cars as Dealership A and half as many trucks. Therefore, the equation for the total cars and trucks sold by Dealership B can be written as:
C + T = 229
Additionally, we can express the relationship between the number of cars and trucks sold by both dealerships as:
C = 2c (twice as many cars as Dealership A)
T = (1/2)t (half as many trucks as Dealership A)
c) To find out how many cars Dealership A sold, we can use the equation from part a:
c + t = 164
Since we don't know the actual values of c and t, we need additional information to solve for them.
d) According to the information provided, Dealership B sold half as many trucks as Dealership A. Using this relationship, we can substitute t/2 for T in the equation from part b:
C + T = 229
C + t/2 = 229
Again, we need additional information to determine the actual values of c and t to find out how many trucks Dealership B sold.
a) Let's assume the number of cars sold by Dealership A is represented by 'x', and the number of trucks sold by Dealership A is represented by 'y'. The total cars and trucks sold by Dealership A can be represented by the equation:
x + y = 164
b) Let's assume the number of cars sold by Dealership B is represented by 'm', and the number of trucks sold by Dealership B is represented by 'n'. We know that Dealership B sells twice as many cars as Dealership A (2x) and half as many trucks as Dealership A (0.5y). The total cars and trucks sold by Dealership B can be represented by the equation:
2x + 0.5y = 229
c) Substituting the first equation into the second equation, we have:
2x + 0.5y = 229
2(164 - y) + 0.5y = 229
328 - 2y + 0.5y = 229
-1.5y = -99
y = 66
So, Dealership A sold 66 trucks.
d) Dealership B sold half as many trucks as Dealership A, which means Dealership B sold half of 66 trucks. Thus, Dealership B sold:
0.5 * 66 = 33 trucks.