Question 163266
First, you need to define your variables:
Let x = number of intermediate cars purchased
then because "twice as many compacts as intermediate cars are purchased":
2x = number of compacts purchased
and finally because "a total of 100 cars" were purchased:
100-3x = full size cars purchased
.
Now, we can derive our equation:
12000(2x) +18000x+ 24000(100-3x) = 1500000 
24000x + 18000x+ 2400000 - 72000x = 1500000 
24x + 18x+ 2400 - 72x = 1500 
2400 - 30x = 1500 
2400 = 30x+1500 
900 = 30x
30 = x (number of intermediate cars)
.
number of compacts:
2x = 2(30) = 60
.
number of full-sized cars:
100-3x = 100-3(30) = 100-90 = 10