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 Dealership A, and sells a total of 300 cars and trucks.

Question

1) How many CARS did Dealership A sell?

2) Considering that Dealership B sold half as many trucks as Dealership A, how many TRUCKS did Dealership B sell?

Answer 1

Let's solve the problem step by step.

1) We know that Dealership A sells a total of 225 cars and trucks. Let's assume that it sells x cars and y trucks. We can set up the equation: x + y = 225.

2) We also know that Dealership B sells twice as many cars and half as many trucks as Dealership A. This means that Dealership B sells 2 times x cars and 0.5 times y trucks. We can set up the second equation: 2x + 0.5y = 300.

Now we have a system of equations:

x + y = 225
2x + 0.5y = 300

To solve this system, we can use the substitution method. Let's solve the first equation for x:

x = 225 - y

Now we substitute this expression for x in the second equation:

2 * (225 - y) + 0.5y = 300
450 - 2y + 0.5y = 300
450 - 300 = 2y - 0.5y
150 = 1.5y
y = 150 / 1.5
y = 100

Now we can substitute the value of y in the first equation to find x:

x + 100 = 225
x = 225 - 100
x = 125

Therefore, Dealership A sold 125 cars and Dealership B sold 100 trucks.