Solving word problems with the matrix method?

Discussion in 'Personal Homework Help' started by Emily Angel, Sep 26, 2017.

  1. Emily Angel

    Emily Angel New Member

    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!

  2. math_celebrity

    math_celebrity Administrator Staff Member

    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

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