1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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)

  2. jcsd
  3. Sep 26, 2006 #2


    User Avatar

    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


    User Avatar

    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


    User Avatar

    Staff: Mentor

    Yeah, see my edit above. That should clear it up.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Using linear Systems to Solve Problems