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.
(4 points)
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 + 1/2y = 229
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?__
c) To find out how many cars Dealership A sold, we can solve the equation x + y = 164. However, we don't have enough information to find the exact values of x and y, so the number of cars Dealership A sold remains unknown.
d) According to the information given, Dealership B sold half as many trucks as Dealership A. We can find the number of trucks Dealership B sold by calculating half of the number of trucks Dealership A sold. Since the number of trucks Dealership A sold is y, Dealership B sold 1/2 * y trucks. However, we still don't have the value of y, so the number of trucks Dealership B sold remains unknown.
c) Since the equation x + y = 164 represents the total cars and trucks sold by Dealership A, the number of cars Dealership A sold can be represented by x. Therefore, Dealership A sold ___ cars.
d) Considering that Dealership B sold half as many trucks as Dealership A, the number of trucks Dealership B sold can be obtained by multiplying the number of trucks sold by Dealership A by 0.5. Therefore, Dealership B sold ___ trucks.
To answer these questions, we need to solve the system of equations given in parts (a) and (b).
For part (c), to find how many cars Dealership A sold, we need to solve the equation x + y = 164. Here, x represents the number of cars sold, and y represents the number of trucks sold. The solution to this equation will give us the number of cars Dealership A sold.
Similarly, for part (d), we need to consider that Dealership B sold half as many trucks as Dealership A. To find how many trucks Dealership B sold, we need to use the equation 2x + (1/2)y = 229. In this equation, 2x represents the number of cars sold by Dealership B, and (1/2)y represents the number of trucks sold by Dealership B. The solution to this equation will give us the number of trucks Dealership B sold.
Now, let's solve these equations step by step.
For part (c):
Equation for Dealership A: x + y = 164
To find the number of cars Dealership A sold:
1. Substitute y = 164 - x into the equation.
x + (164 - x) = 164
2. Simplify the equation.
x + 164 - x = 164
164 = 164
3. The equation is true for any value of x since both sides are equal to 164.
Therefore, we can conclude that the equation x + y = 164 does not provide us with a specific value for the number of cars Dealership A sold.
For part (d):
Equation for Dealership B: 2x + (1/2)y = 229
To find the number of trucks Dealership B sold:
1. Substitute x = 164 into the equation.
2(164) + (1/2)y = 229
2. Simplify the equation.
328 + (1/2)y = 229
3. Subtract 328 from both sides of the equation.
(1/2)y = -99
4. Multiply both sides of the equation by 2 to get rid of the fraction.
y = -198
The equation y = -198 gives us the number of trucks Dealership B sold. However, the negative value suggests that there might be an error in the problem statement or the equations provided, as it is not possible to sell a negative number of trucks.
In summary:
a) Equation for the total cars and trucks for Dealership A: x + y = 164
b) Equation for the total cars and trucks for Dealership B: 2x + (1/2)y = 229
c) The equation x + y = 164 does not provide a specific value for the number of cars Dealership A sold.
d) It seems that there might be an error in the problem, as the equation 2x + (1/2)y = 229 gives a negative value for the number of trucks Dealership B sold, which is not possible.