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:
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 C represent the number of cars sold by Dealership A and T represent the number of trucks sold by Dealership A. The equation for the total cars and trucks for Dealership A is:
C + T = 164
b) Let C' represent the number of cars sold by Dealership B and T' represent the number of trucks sold by Dealership B. The equation for the total cars and trucks for Dealership B is:
C' + T' = 229
c) Dealership A sold 164 - T trucks. There is no specific information given about the number of cars sold by Dealership A, so we cannot determine the exact number of cars dealership A sold.
d) Dealership B sold half as many trucks as Dealership A, so T' = T/2.
a) Let's represent the number of cars sold by Dealership A as 'x' and the number of trucks sold as 'y'. The total cars and trucks sold by Dealership A is 164, so the equation is:
x + y = 164
b) According to the information provided, Dealership B sells twice as many cars and half as many trucks as Dealership A. Let's represent the number of cars sold by Dealership B as 'x' and the number of trucks sold as 'y'. The total cars and trucks sold by Dealership B is 229, so the equation is:
2x + 0.5y = 229
c) To find out how many cars Dealership A sold, we need to solve the equation x + y = 164 for x. Let's isolate x:
x = 164 - y
d) Considering that Dealership B sold half as many trucks as Dealership A, we can set up an equation to find the number of trucks sold by Dealership B. Since x represents the number of cars sold by both dealerships, we can use x in the equation:
0.5y = x
We already know from equation (c) that x = 164 - y, so substituting this value into the equation, we get:
0.5y = 164 - y
Now we can solve for y to find the number of trucks sold by Dealership B.
a) Let's assume that the number of cars sold by Dealership A is denoted by "C" and the number of trucks sold by Dealership A is denoted by "T". Based on the given information, we know that the total number of cars and trucks sold by Dealership A is 164.
So, the equation for the total cars and trucks sold by Dealership A can be written as:
C + T = 164
b) Similarly, let's assume that the number of cars sold by Dealership B is denoted by "C'" and the number of trucks sold by Dealership B is denoted by "T'". We are told that Dealership B sells twice as many cars and half as many trucks as Dealership A, and the total number of cars and trucks sold by Dealership B is 229.
So, the equation for the total cars and trucks sold by Dealership B can be written as:
C' + T' = 229
c) To find the number of cars sold by Dealership A, we need to substitute the given information into the equation for Dealership A:
C + T = 164
We are not given any specific values for C or T, but since we know that Dealership B sells twice as many cars as Dealership A, we can denote the number of cars sold by Dealership A as "x". Therefore, the number of cars sold by Dealership B would be "2x".
So, the equation becomes:
x + 2x = 164
Combining like terms:
3x = 164
To isolate x, divide both sides of the equation by 3:
x = 164/3
Therefore, Dealership A sold approximately 54.67 cars.
d) The question states that Dealership B sold HALF as many trucks as Dealership A. Since we know that Dealership A sold approximately 54.67 cars, we can denote the number of trucks sold by Dealership A as "y". Therefore, the number of trucks sold by Dealership B would be "y/2".
Since we don't know the exact value of y, we cannot determine the exact number of trucks sold by Dealership B without more information.