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.
a) An equation for the total cars and trucks for Dealership A:
options: x+y=164, x+y=229, x+y=393
b) An equation for the total cars and trucks for Dealership B:
options: 1/2x+2y=164, 2x+1/2y=229, 1/2x+1/2y=229
c) How many cars did Dealership A sell?
options: 66, 132, 196, 98
d) Considering that Dealership B sold HALF as many trucks as Dealership A, how many trucks did Dealership B sell?
options: 33, 66, 49, 98
a) An equation for the total cars and trucks for Dealership A:
x + y = 164
The equation represents the total cars (x) and trucks (y) sold by Dealership A.
b) An equation for the total cars and trucks for Dealership B:
2x + (1/2)y = 229
The equation represents that Dealership B sold twice as many cars (2x) and half as many trucks ((1/2)y) as Dealership A, totaling to 229 cars and trucks.
c) To find how many cars Dealership A sold, we can solve the equation x + y = 164. There are multiple methods to solve this, but let's use substitution:
We can assume that x is the number of cars sold, and y is the number of trucks sold.
From equation a), we can write x = 164 - y.
Substituting this value of x in equation b), we have:
2(164 - y) + (1/2)y = 229
328 - 2y + (1/2)y = 229
328 - 229 = (3/2)y
99 = (3/2)y
Multiplying both sides by 2/3, we get:
66 = y
Therefore, Dealership A sold 66 trucks.
To determine how many cars were sold by Dealership A, we can substitute the value of y (66) in equation a):
x + 66 = 164
x = 164 - 66
x = 98
Therefore, Dealership A sold 98 cars.
d) Since Dealership B sold half as many trucks as Dealership A, and Dealership A sold 66 trucks, Dealership B sold 66/2 = 33 trucks.
The answers would be:
c) How many cars did Dealership A sell?
Option: 98
d) Considering that Dealership B sold HALF as many trucks as Dealership A, how many trucks did Dealership B sell?
Option: 33
a) An equation for the total cars and trucks for Dealership A:
The equation for the total cars and trucks sold by Dealership A is:
x + y = 164
b) An equation for the total cars and trucks for Dealership B:
Since Dealership B sells twice as many cars and half as many trucks as Dealership A, the equation for Dealership B is:
2x + (1/2)y = 229
c) How many cars did Dealership A sell?
To find the number of cars Dealership A sold, we can solve the equation x + y = 164 for x:
x + y = 164
x = 164 - y
Now, substitute this value for x into the equation 2x + (1/2)y = 229:
2(164 - y) + (1/2)y = 229
328 - 2y + (1/2)y = 229
(1/2)y - 2y = 229 - 328
(-3/2)y = -99
y = (-99)/((-3/2))
y = 66
Since x + y = 164, we can substitute y = 66 into this equation to find x:
x + 66 = 164
x = 164 - 66
x = 98
Therefore, Dealership A sold 98 cars.
c) Considering that Dealership B sold HALF as many trucks as Dealership A, how many trucks did Dealership B sell?
Since Dealership A sold 66 trucks (as found in the previous step), Dealership B sold half as many trucks, which is:
(1/2) * 66 = 33
Therefore, Dealership B sold 33 trucks.
a) The equation for the total cars and trucks for Dealership A would be x + y = 164, where x represents the number of cars and y represents the number of trucks.
b) The equation for the total cars and trucks for Dealership B can be derived from the given information: Dealership B sells twice as many cars as Dealership A (2x) and half as many trucks as Dealership A (0.5y). So, the equation would be 2x + 0.5y = 229.
c) To find out how many cars Dealership A sold, we can substitute the equation from part (a) into the equation from part (c). Solving for x:
x + y = 164
x = 164 - y
Substituting this back into the equation, we get:
(164 - y) + y = 164
164 - y + y = 164
164 = 164
Therefore, the equation is consistent and does not provide any specific value for x. It means that the number of cars sold by Dealership A could be any value as long as the sum of cars and trucks is 164.
c) The options given for how many cars Dealership A sold are 66, 132, 196, and 98. However, based on the equation, there is no specific answer given. Therefore, it is not possible to determine exactly how many cars Dealership A sold from the given information.
d) It is mentioned that Dealership B sold half as many trucks as Dealership A. Since the number of trucks sold by Dealership A is not determined directly, we cannot calculate the exact number of trucks sold by Dealership B. Therefore, it is not possible to determine how many trucks Dealership B sold from the given information. The options provided (33, 66, 49, and 98) cannot be determined as the answer.