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A company owns two dealerships, both of which sell cars and trucks. Dealership A sells a total of 225 cars and trucks. Dealership B sells twice as many cars and half as many trucks as the Dealership A, and sells a total of 300 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) Given the fact that Dealership B sold half as many trucks as Dealership A, how many trucks did Dealership B sell?
a) Let x be the number of cars and y be the number of trucks sold by Dealership A. Since Dealership A sold a total of 225 cars and trucks, the equation can be written as:
x + y = 225
b) Let a be the number of cars and b be the number of trucks sold by Dealership B. Since Dealership B sold twice as many cars and half as many trucks as Dealership A, the equation can be written as:
a + b = 300
c) To find the number of cars sold by Dealership A, we can substitute y = 225 - x into the equation a + b = 300:
x + (225 - x) = 300
Simplifying the equation, we get:
225 = 300
Therefore, Dealership A sold 225 cars.
d) Given that Dealership B sold half as many trucks as Dealership A, we can substitute y/2 for b in the equation a + b = 300:
x + (y/2) = 300
Since we know that x = 225, we can substitute it into the equation:
225 + (y/2) = 300
Simplifying the equation, we get:
(y/2) = 75
Multiplying both sides by 2, we get:
y = 150
Therefore, Dealership B sold 150 trucks.
a) The equation for the total cars and trucks sold by Dealership A can be represented as:
Total cars and trucks = 225
b) The equation for the total cars and trucks sold by Dealership B can be represented as:
Total cars and trucks = 300
c) To find the number of cars sold by Dealership A, we can subtract the number of trucks sold from the total. Since the problem does not provide specific information about the ratio of cars to trucks at Dealership A, we cannot determine the exact number of cars. We can only say that the number of cars sold by Dealership A plus the number of trucks sold equals 225.
d) Given that Dealership B sold half as many trucks as Dealership A, we can say that the number of trucks sold by Dealership B is half of the number of trucks sold by Dealership A. Since we do not have the exact number of trucks sold by Dealership A, we cannot determine the exact number of trucks sold by Dealership B.
To answer these questions, we can use algebraic equations. Let's define variables to represent the number of cars and trucks sold by each dealership.
a) An equation for the total cars and trucks for Dealership A:
Let's assume the number of cars sold by Dealership A is represented by 'C', and the number of trucks sold is represented by 'T'.
Therefore, we can write the equation as:
C + T = 225
b) An equation for the total cars and trucks for Dealership B:
Since Dealership B sells twice as many cars as Dealership A and half as many trucks as Dealership A, we can write the equation:
2C + (1/2)T = 300
c) How many cars did Dealership A sell?
To find the number of cars sold by Dealership A, we can substitute the known values into equation (a):
C + T = 225
Since we don't know the exact values of C and T, we can't directly find the number of cars, C, that Dealership A sold. However, we can solve for one variable in terms of the other.
Let's solve equation (a) for T in terms of C:
T = 225 - C
Now we have an expression for T in terms of C. We can substitute this expression into equation (b) and solve for the number of cars:
2C + (1/2)(225 - C) = 300
Simplifying the equation:
2C + (112.5 - 0.5C) = 300
1.5C + 112.5 = 300
1.5C = 300 - 112.5
1.5C = 187.5
C = 187.5 / 1.5
C = 125
Therefore, Dealership A sold 125 cars.
d) Given the fact that Dealership B sold half as many trucks as Dealership A
From equation (a), we have T = 225 - C
Since Dealership B sold half as many trucks as Dealership A, we can write an equation:
T = (1/2)(225 - C)
Now we have an expression for T in terms of C. We can substitute this expression into equation (b) and solve for the number of trucks:
2C + (1/2)((225 - C)/2) = 300
Simplifying the equation:
2C + (225-C)/4 = 300
Multiplying through by 4 to eliminate the fraction:
8C + (225 - C) = 1200
7C + 225 = 1200
7C = 1200 - 225
7C = 975
C = 975 / 7
C = 139.29 (approx.)
However, since we are dealing with a real-life scenario where you can't sell a fraction of a car or truck, we need to round down to the nearest whole number. Therefore, Dealership B sold 139 trucks.
To summarize:
a) An equation for the total cars and trucks for Dealership A: C + T = 225
b) An equation for the total cars and trucks for Dealership B: 2C + (1/2)T = 300
c) Dealership A sold 125 cars.
d) Dealership B sold 139 trucks.