SOLUTION: A car rental as allocated $1.5million to buy a fleet of cars consisting od compact, intermediate and full size cars. Compacts cost $12000, intermediate coast 18,000 and full size c

Question 163266: A car rental as allocated $1.5million to buy a fleet of cars consisting od compact, intermediate and full size cars. Compacts cost $12000, intermediate coast 18,000 and full size cost $24,000 each. If twice as many compacts as intermediate cars are purchased and the total number is 100 determine how many cars of each type will be purchased(assume that the entire budget will be used)
I'm not sure whether my equation is right can you please help me?
This is what I have: let x represent compacts, let y represent intermediate & let z represent full size. therfore,
First equation is 12000x +18000+ 24000 = 1.500000
Second equation is x= 2y + 100

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
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

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