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
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) Let's denote the number of cars sold by Dealership A as x, and the number of trucks sold by Dealership A as y. Therefore, the equation for the total cars and trucks sold by Dealership A is x + y = 164.
b) Let's denote the number of cars sold by Dealership B as 2x (twice as many as Dealership A), and the number of trucks sold by Dealership B as (1/2)y (half as many as Dealership A). Therefore, the equation for the total cars and trucks sold by Dealership B is 2x + (1/2)y = 229.
c) From the equation for Dealership A, x + y = 164, we don't have enough information to determine how many cars Dealership A sold. We would need another equation or more information to solve for x.
d) From the equation for Dealership B, 2x + (1/2)y = 229, we cannot directly determine the number of trucks sold by Dealership B because we do not know the values of x and y. We would need another equation or more information to solve for (1/2)y.
a) Let's let "x" represent the number of cars sold by Dealership A, and "y" represent the number of trucks sold by Dealership A. The equation for the total cars and trucks for Dealership A can be written as:
x + y = 164
b) Dealership B sells twice as many cars and half as many trucks as Dealership A. Therefore, if Dealership A sold "x" cars and "y" trucks, Dealership B sold 2x cars and 0.5y trucks. The equation for the total cars and trucks for Dealership B can be written as:
2x + 0.5y = 229
c) We can solve the equation for Dealership A to find the number of cars sold by Dealership A:
x + y = 164
Rearranging the equation:
x = 164 - y
d) According to the information given, Dealership B sold half as many trucks as Dealership A. So, y (number of trucks sold by Dealership B) = 0.5y (number of trucks sold by Dealership A). This means the number of trucks sold by Dealership B is half the number of trucks sold by Dealership A.
To solve this problem, we need to break it down into steps and use algebraic expressions to represent the information given.
a) To find the equation for the total cars and trucks for Dealership A, we'll let "x" be the number of cars sold by Dealership A and "y" be the number of trucks sold by Dealership A. Since they sell a total of 164 cars and trucks, we can write the equation as:
x + y = 164
b) To find the equation for the total cars and trucks for Dealership B, we know that they sell twice as many cars and half as many trucks as Dealership A. So, if Dealership A sells "x" cars, Dealership B sells 2x cars. And if Dealership A sells "y" trucks, Dealership B sells y/2 trucks. Adding these together, we get:
2x + y/2 = 229
c) To find out how many cars Dealership A sold, we can use the equation from part (a). Since the equation is x + y = 164, we can solve for x by substituting y = 164 - x:
x + (164 - x) = 164
x + 164 - x = 164
164 = 164
Therefore, the equation is satisfied by any value of x, meaning we can't determine the specific number of cars Dealership A sold just based on the information given.
d) To find out how many trucks Dealership B sold, we need to use the equation from part (b). Since the equation is 2x + y/2 = 229, let's solve for y by substituting 2x = 229 - y/2:
2x + y/2 = 229
4x + y = 458 - y
5x = 458 - y
y = 458 - 5x
Unfortunately, we don't have an equation to solve for the value of "x" in order to find the exact number of trucks Dealership B sold.