Solving word problems with the matrix method?

[Emily Angel]

Hello everyone.
I am stuck on a work question that we are required to solve using the matrix (or Gauss-Jordan) method.

"A car rental company wants to buy 100 new cars. Compact cars cost $12,000 each,
intermediate size cars cost $18,000 each, full size cars cost $24,000 each, and the company
has a budget of $1,500,000. If they purchase twice as many compact cars as intermediate
sized cars, determine the number of cars of each type that they buy, assuming they
spend the entire budget."
​

I am fairly certain that I could solve this easily, except I cannot figure out the proper three equations that correspond to this question. I someone could help me figure them out, it would be greatly appreciated!

 

[math_celebrity]

Let c be the cost of compact cars, i be the cost of intermediate cards, and f be the cost of full-size cars. We have the following equations:

• c + i + f = 100
• 12,000c + 18,000i + 24,000 f = 1,500,000
• c = 2i