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Using linear Systems to Solve Problems

  1. Sep 26, 2006 #1
    Simple Question, just need help establising second formula

    Premium gasoline sells for 78.9/L. Regular gas sells of 71.9/L. To boost sales, a middle octane gasoline is formed by mixing premuium and regular. If 1000 L of this middle octane gas is prodcued ,and is sold at 73.9/L, then how much of each type of gasoline can you assume was used in the mixture. (units are in cents)

    i got my first formula

    x + y = 1000

    its the second formula that confuses me

    this is my incorrect one
    78.9 x + 71.9 y = 73.9 (1000)

    help
     
  2. jcsd
  3. Sep 26, 2006 #2

    berkeman

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    Staff: Mentor

    Looks okay to me. The next step is to realize that y = 1000 - x, and substitute that into the 2nd equation.
     
  4. Sep 26, 2006 #3
    is that 2nd equation is right

    the answer is 600 L of premium, and 400 L or regualar

    that equation doenst get that
     
  5. Sep 26, 2006 #4

    berkeman

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    Staff: Mentor

    I think it's just your algebra. Try solving this form to find the percentage of premium (your x variable):

    [tex]78.9 x + 71.9 (1-x) = 73.9[/tex]

    Distribute x and solve. No calculator required.


    EDIT -- I recast your x into the percentage. In your initial equation, it is the percentage multiplied by 1000L. Sorry for any confusion.
     
    Last edited: Sep 26, 2006
  6. Sep 26, 2006 #5
    got x=2/7

    which is obviously not 600.

    still something must be wrong
     
  7. Sep 26, 2006 #6

    berkeman

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    Staff: Mentor

    Yeah, see my edit above. That should clear it up.
     
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