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". Since Dealership A sells a total of 164 cars and trucks, we can write the equation:
x + y = 164
b) Let's denote the number of cars sold by Dealership B as "a" and the number of trucks sold by Dealership B as "b". Since Dealership B sells twice as many cars as Dealership A and half as many trucks as Dealership A, we can write the equation:
a + b = 229
c) We know that Dealership A sells "x" cars. Since the equation from part a) is x + y = 164, we can substitute the value of x into this equation to solve for y:
x + y = 164
x + y = 164
164 + y = 164
y = 164 - x
So, Dealership A sold 164 - x cars.
d) We know that Dealership B sold half as many trucks as Dealership A. Since the equation from part a) is x + y = 164, we can substitute the value of y into this equation to solve for x:
x + y = 164
x + (164 - x) = 164
164 - x = 164 - x
0 = 0
Since this equation is always true, it means that the value of y can be any number. Therefore, we cannot determine the number of trucks sold by Dealership B based on the given information.
a) An equation for the total cars and trucks for Dealership A:
Let's assume the number of cars sold by Dealership A is C and the number of trucks sold is T.
The total cars and trucks sold by Dealership A can be represented by the equation: C + T = 164.
b) An equation for the total cars and trucks for Dealership B:
Let's assume the number of cars sold by Dealership B is C' and the number of trucks sold is T'.
According to the given information, Dealership B sells twice as many cars and half as many trucks as Dealership A.
So, the equation for the total cars and trucks sold by Dealership B can be written as: 2C' + 0.5T' = 229.
c) How many cars did Dealership A sell?:
From equation (a), we know that C + T = 164.
The number of cars sold by Dealership A is represented by C.
Thus, Dealership A sold C cars.
d) Considering that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?:
From the given information, we know that T' = 0.5T.
Since Dealership B sold half as many trucks as Dealership A, the number of trucks sold by Dealership B is half of the number of trucks sold by Dealership A.
So, Dealership B sold T' trucks.
a) To find the equation for the total cars and trucks sold by Dealership A, we can use the given information that Dealership A sold a total of 164 cars and trucks. We can represent the number of cars sold by "x" and the number of trucks sold by "y". The equation would be: x + y = 164.
b) To find the equation for the total cars and trucks sold by Dealership B, we can use the given information that Dealership B sells twice as many cars and half as many trucks as Dealership A, and sells a total of 229 cars and trucks. Using the same variables, we can write the equation as: 2x + (1/2)y = 229.
c) To determine how many cars Dealership A sold, we can solve the equation x + y = 164 for x. We can subtract y from both sides of the equation, yielding x = 164 - y. Since we were given the total number of cars and trucks sold by Dealership A as 164, we can substitute this value into the equation: 164 - y = number of cars sold by Dealership A.
d) Considering that Dealership B sold half as many trucks as Dealership A, we can express the number of trucks sold by Dealership B as (1/2)y. We can substitute this value into the equation 2x + (1/2)y = 229 to find the number of trucks sold by Dealership B: 2x + (1/2)y = 229.