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) An equation for the total cars and trucks for Dealership A:
Let x be the number of cars sold by Dealership A
Let y be the number of trucks sold by Dealership A
The equation is: x + y = 164
b) An equation for the total cars and trucks for Dealership B:
Since Dealership B sells twice as many cars as A and half as many trucks as A, let's represent that with the following equations:
2x for cars sold by Dealership B
0.5y for trucks sold by Dealership B
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.
From the given information, there is no specific data about how many trucks or cars were sold by Dealership A. Therefore, it is not possible to determine how many cars Dealership A sold without additional information.
d) Considering that Dealership B sold half as many trucks as Dealership A, we can assume that y/2 is equal to the number of trucks sold by Dealership B.
From the given information, there is no specific data about the number of trucks sold by Dealership A. Without knowing the value of y, it is not possible to determine how many trucks Dealership B sold.
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'.
Therefore, the equation will be:
c + t = 164
b) An equation for the total cars and trucks for Dealership B:
Given that Dealership B sells twice as many cars and half as many trucks as Dealership A, we can set up the following equation:
2c + (1/2)t = 229
c) How many cars did Dealership A sell?
From equation (a), we have c + t = 164.
Since we don't know the exact values of c and t, we can't determine the number of cars Dealership A sold without more information.
d) Considering that Dealership B sold half as many trucks as Dealership A, we can set up the equation as:
t/2 = (1/2)t
This implies that the number of trucks sold by Dealership B is equal to the number of trucks sold by Dealership A, which means Dealership B sold the same number of trucks as Dealership A sold. However, without the specific values of c and t, we can't determine the exact number of trucks Dealership B sold.
a) To find the equation for the total cars and trucks sold by Dealership A, we'll let C represent the number of cars sold and T represent the number of trucks sold. Since we're given that Dealership A sold a total of 164 cars and trucks, we can write the equation:
C + T = 164
b) To find the equation for the total cars and trucks sold by Dealership B, we'll use the information that Dealership B sold twice as many cars and half as many trucks as Dealership A. Since we know that Dealership A sold C cars, and Dealership B sold twice as many cars and half as many trucks as Dealership A, we can write the equation:
2C + (1/2)T = 229
c) To find the number of cars Dealership A sold, we can substitute the value of T as 164 - C in the equation from part a:
C + (164 - C) = 164
By simplifying the equation:
C + 164 - C = 164
Cancelling out C:
164 = 164
This equation is always true, meaning the value of C doesn't matter. Therefore, we can't determine the exact number of cars Dealership A sold just from this information.
d) As stated earlier, Dealership B sold half as many trucks as Dealership A. So, the number of trucks Dealership B sold is half of the number of trucks Dealership A sold. Since we know that Dealership A sold T trucks, Dealership B sold (1/2)T trucks.