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 2x (twice as many as Dealership A) and the number of trucks sold by Dealership B as y/2 (half as many as Dealership A). Since Dealership B sells a total of 229 cars and trucks, we can write the equation:
2x + y/2 = 229
c) To find out how many cars Dealership A sold, we need to solve equation (a) for x.
x = 164 - y
d) Since Dealership B sold half as many trucks as Dealership A, the number of trucks sold by Dealership B would be y/2.
a) An equation for the total cars and trucks for Dealership A:
Let c be the number of cars sold by Dealership A.
Let t be the number of trucks sold by Dealership A.
We know that c + t = 164.
b) An equation for the total cars and trucks for Dealership B:
Dealership B sells twice as many cars as Dealership A and half as many trucks.
So the number of cars sold by Dealership B is 2c.
And the number of trucks sold by Dealership B is 0.5t.
Therefore, 2c + 0.5t = 229.
c) How many cars did Dealership A sell?
From the equation c + t = 164, we can solve for c:
c = 164 - t.
We don't have enough information to determine the exact number of cars sold by Dealership A.
d) Considering that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?
From the equation 2c + 0.5t = 229, we can substitute the value of c from equation (c) into equation (b):
2(164 - t) + 0.5t = 229.
Simplifying the equation:
328 - 2t + 0.5t = 229.
-1.5t = -99.
Dividing by -1.5:
t = 66.
Therefore, Dealership B sold 66 trucks.
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 sold 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'.
According to the given information, Dealership B sells twice as many cars as Dealership A and half as many trucks as Dealership A. Therefore, we can write the equations:
a = 2x (twice as many cars as Dealership A)
b = 0.5y (half as many trucks as Dealership A)
Since Dealership B sold a total of 229 cars and trucks, we can also write:
a + b = 229
c) To find out how many cars Dealership A sold, we need to substitute the given values into the equation from part (a).
x + y = 164
From the given information, we know that Dealership A sold a total of 164 cars and trucks. Therefore, we have one equation with two variables.
d) To find out how many trucks Dealership B sold, we need to substitute the given values into the equation from part (b).
a + b = 229
From the given information, we know that Dealership B sold a total of 229 cars and trucks. Therefore, we have one equation with two variables.