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 & sell?
d) Considering that Dealership B sold half as many trucks as Dealership A, how
many trucks did Dealership B sell?
a) Let C be the total number of cars at Dealership A and T be the total number of trucks at Dealership A. Since Dealership A sells a total of 164 cars and trucks, the equation for the total cars and trucks for Dealership A is C + T = 164.
b) Let C' be the total number of cars at Dealership B and T' be the total number of trucks at Dealership B. Since Dealership B sells twice as many cars and half as many trucks as Dealership A, the equation for the total cars and trucks for Dealership B is 2C + 0.5T = 229.
c) To solve for the number of cars Dealership B sells, we can use the equation for the total cars and trucks for Dealership B. Since we know that Dealership B sells 229 cars and trucks, we substitute this value into the equation: 2C + 0.5T = 229.
d) Since Dealership B sold half as many trucks as Dealership A, we can set T' = 0.5T. To solve for the number of trucks Dealership B sells, we substitute this relationship into the equation for the total cars and trucks for Dealership B: 2C + 0.5(0.5T) = 229.
To solve this problem, we need to use algebra to create equations and solve them.
a) Let's create an equation for the total cars and trucks sold by Dealership A.
Let's assume that the number of cars sold by Dealership A is "x" and the number of trucks sold by Dealership A is "y." According to the information provided, the total number of cars and trucks sold by Dealership A is 164. Therefore, we can write the equation as:
x + y = 164
b) Now let's create an equation for the total cars and trucks sold by Dealership B.
We know that Dealership B sells twice as many cars and half as many trucks as Dealership A. From part a), we know that the number of cars sold by Dealership A is x. The number of cars sold by Dealership B would be twice as many, so it would be 2x. The number of trucks sold by Dealership B would be half as many as Dealership A, so it would be y/2. In total, the number of cars and trucks sold by Dealership B is 229. Therefore, the equation would be:
2x + (y/2) = 229
c) To find out how many cars Dealership B sold, we substitute the value of x into equation b) and solve for x. Once we have the value of x, we will know how many cars Dealership B sold.
d) To find out how many trucks Dealership B sold, we substitute the value of y into equation b) and solve for y. Once we have the value of y, we will know how many trucks Dealership B sold.
a) Let's denote the number of cars sold by Dealership A as cA and the number of trucks sold by Dealership A as tA. We are given that the total number of cars and trucks sold by Dealership A is 164. Therefore, the equation for the total cars and trucks for Dealership A can be written as:
cA + tA = 164
b) We are given that Dealership B sells twice as many cars and half as many trucks as Dealership A. Let's denote the number of cars sold by Dealership B as cB and the number of trucks sold by Dealership B as tB. We can write the equation for the total cars and trucks for Dealership B using the information given:
cB + tB = 229
c) We need to find the number of cars sold by Dealership B. From the information given, we know that Dealership B sells twice as many cars as Dealership A. So, cB = 2cA.
Substituting this into the equation for Dealership B, we have:
2cA + tB = 229
Since we don't know the value of cA or tB, we need more information to determine the exact number of cars sold by Dealership B.
d) We are also given that Dealership B sells half as many trucks as Dealership A. So, tB = 0.5tA.
Substituting this into the equation for Dealership B, we have:
cB + 0.5tA = 229
Again, we need more information to determine the exact number of trucks sold by Dealership B.