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)

Question

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?_____

Answer 1

a) An equation for the total cars and trucks for Dealership A:
Let's assume that the number of cars Dealership A sold is represented by 'x' and the number of trucks Dealership A sold is represented by 'y'.
From the given information, we know that Dealership A sold a total of 164 cars and trucks. So, the equation for the total cars and trucks for Dealership A can be written as:
x + y = 164

b) An equation for the total cars and trucks for Dealership B:
From the given information, we know that Dealership B sold twice as many cars and half as many trucks as Dealership A.
Let's assume that the number of cars Dealership B sold is represented by 'm' and the number of trucks Dealership B sold is represented by 'n'.
So, we can write the following equations:
m = 2x (Dealership B sold twice as many cars as Dealership A)
n = 0.5y (Dealership B sold half as many trucks as Dealership A)

To find the total number of cars and trucks for Dealership B, we can write the equation:
m + n = 229

c) How many cars did Dealership A sell?
From equation (a), we have x + y = 164
Since the question asks about the number of cars Dealership A sold, we need to isolate x.
x = 164 - y

d) Considering that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?
From equation (b), we have n = 0.5y
Since the question asks about the number of trucks Dealership B sold, we need to find the value of n when y = ? (from equation (c), we found that x = 164 - y, so y represents the number of trucks Dealership A sold).
Substituting y = 164 - y into the equation n = 0.5y, we get:
n = 0.5(164 - y)

We do not have enough information to determine the exact number of trucks Dealership B sold, as it depends on the value of y (the number of trucks Dealership A sold).