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? 98 d) Considering that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?
To solve the equation x + y = 164, we need to substitute the values of x and y with the given information:
We know that Dealership A sold a total of 164 cars and trucks, so x = 164.
To find the value of y, we need to use the information given in part (b), which states that Dealership B sold twice as many cars and half as many trucks as Dealership A. So, we can write the equation for Dealership B as:
2x + (1/2)y = 229.
Using the equation from part (a), x + y = 164, we can substitute the value of x into the equation for Dealership B:
2(164) + (1/2)y = 229.
Now, we can solve for y:
328 + (1/2)y = 229,
(1/2)y = 229 - 328,
(1/2)y = -99,
y = -99 * (2/1),
y = -198.
Since it doesn't make sense for a dealership to sell a negative number of cars or trucks, we can conclude that there was an error in the calculations or given information. Please revise the question.
c) Dealership A sold 98 cars.
d) Dealership B sold 33 trucks.
To solve this problem, let's break it down step by step:
a) An equation for the total cars and trucks for Dealership A:
Let's assume the number of cars Dealership A sold is represented by x, and the number of trucks is y.
We are given that the total number of cars and trucks Dealership A sold is 164. Therefore, the equation for Dealership A is:
x + y = 164
b) An equation for the total cars and trucks for Dealership B:
We are told that Dealership B sells twice as many cars as Dealership A and half as many trucks. The number of cars Dealership B sold is represented by 2x (twice the number of cars sold by Dealership A), and the number of trucks is represented by 1/2y (half the number of trucks sold by Dealership A).
We are also given that the total number of cars and trucks Dealership B sold is 229. Therefore, the equation for Dealership B is:
2x + 1/2y = 229
c) How many cars did Dealership A sell?
We have the equation x + y = 164 for Dealership A. To find the number of cars Dealership A sold, we can solve this equation. Since there is no information about the number of trucks sold separately, we cannot determine the exact number of cars Dealership A sold.
d) Considering that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?
We have the equation 2x + 1/2y = 229 for Dealership B. Since we know that Dealership B sells half as many trucks as Dealership A, we can substitute y with 1/2y in equation a) to get:
x + (1/2)y = 164
Now we have a system of equations:
x + y = 164
x + (1/2)y = 164
By solving this system of equations, we can find the values of x and y, which represent the number of cars and trucks sold by Dealership A.