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: _ ( x+y= 229 , x+y=393 , x+y= 164 )
b) An equation for the total cars and trucks for Dealership B: _ ( 1/2x + 2y=164 , 2x+1/2y= 229 , 1/2x+1/2y = 229 )
c) How many cars did Dealership A sell? _ ( 196, 66, 132, 98 )
d) Considering that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell? _ ( 49, 66, 33, 98 )
a) An equation for the total cars and trucks for Dealership A: x + y = 164
b) An equation for the total cars and trucks for Dealership B: 2x + (1/2)y = 229
c) To find out how many cars Dealership A sold, we can solve the equation x + y = 164 for x.
Substituting x = 164 - y into equation b), we get:
2(164 - y) + (1/2)y = 229
328 - 2y + (1/2)y = 229
Multiply through by 2 to get rid of fractions:
656 - 4y + y = 458
-3y = -198
Dividing by -3, we find:
y = 66
So, Dealership A sold 66 cars.
d) Dealership B sold half as many trucks as Dealership A, so to find out how many trucks Dealership B sold, we take half of the number of trucks sold by Dealership A.
Dealership A sold y = 66 trucks.
Therefore, Dealership B sold (1/2)(66) = 33 trucks.
a) An equation for the total cars and trucks for Dealership A: x + y = 164
b) An equation for the total cars and trucks for Dealership B: 2x + (1/2)y = 229
c) Solving equation (a) we have x + y = 164
Subtracting y from both sides we have x = 164 - y
Substituting this into equation (b) we have:
2(164 - y) + (1/2)y = 229
Distributing the 2 we have 328 - 2y + (1/2)y = 229
Combining like terms we have 328 - (3/2)y = 229
Subtracting 328 from both sides we have -(3/2)y = -99
Dividing by -(3/2) we have y = 66
Substituting this value of y back into equation (a) we have x + 66 = 164
Subtracting 66 from both sides we have x = 98
Therefore, Dealership A sold 98 cars.
d) Dealership B sold half as many trucks as Dealership A, so if Dealership A sold 66 trucks, Dealership B sold 66/2 = 33 trucks.
a) An equation for the total cars and trucks for Dealership A:
Let's assign variables for the number of cars and trucks sold by Dealership A. Let x represent the number of cars and y represent the number of trucks.
Since Dealership A sells a total of 164 cars and trucks, we can create the equation:
x + y = 164
b) An equation for the total cars and trucks for Dealership B:
Dealership B sells twice as many cars as Dealership A and half as many trucks. Let's again use x to represent the number of cars and y to represent the number of trucks.
Since Dealership B sells a total of 229 cars and trucks, we can create another equation:
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.
There are multiple methods to solve this equation:
1. Substitution Method:
Let's solve for x by subtracting y from both sides of the equation:
x = 164 - y
Now we substitute this value of x into the equation x + y = 164:
(164 - y) + y = 164
164 - y + y = 164
164 = 164
The equation is satisfied regardless of the value of y. This means that the value of x can be anything. Therefore, there is not enough information to determine the exact number of cars Dealership A sold.
However, we can find the range of possible values for x by assuming the extreme cases:
If y = 0 (no trucks sold), then x = 164 - 0 = 164. This means Dealership A sold a maximum of 164 cars.
If x = 0 (no cars sold), then y = 164 - 0 = 164. This means Dealership A sold a maximum of 164 trucks.
So, Dealership A sold between 0 and 164 cars.
d) Considering that Dealership B sold half as many trucks as Dealership A, we can find the number of trucks Dealership B sold.
Since we don't know the exact number of trucks Dealership A sold, we'll use a general variable, let's say z, to represent the number of trucks sold by Dealership A.
If Dealership B sold half as many trucks as Dealership A, then the number of trucks Dealership B sold would be (1/2)z.
We can substitute this value into the equation 2x + (1/2)y = 229:
2x + (1/2)y = 229
2x + (1/2)(1/2)z = 229
2x + z/4 = 229
However, without the specific value of z, we cannot find the exact number of trucks Dealership B sold. There is not enough information given to determine the answer.