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Homework Help: Algebra and %

  1. Sep 6, 2004 #1
    How much water must be added to a gallon of alcohol 75% pure to make a mixture 15% pure ?


    The book I'm reading has given this formula : 0.75/(n+1)= 0.15 while n is the number of gallons to be added.
    I don't understand where the heck the formula comes from :confused:
    Can you help me with this problem ?
    Thanks
     
  2. jcsd
  3. Sep 6, 2004 #2
    1 * 0.75 = (n+1) * 0.15 seems like a more understandable form to me.

    basically, above sais that the (absolute) ammount of alcohol is the same in both mixtures.
     
  4. Sep 6, 2004 #3
    That formula comes from this one--a more general form:

    [tex]C_f(V_1+V_2+\cdots+V_n)=C_1V_1+C_2V_2+\cdots+C_nV_n[/tex]

    Where C is concentration and V is volume.

    Now, using you original numbers I can do this:

    [tex]15\%(1gal+V_2)=75\%(1gal)+0\%V_2[/tex]

    Which can be rewritten into the form you first asked about:

    [tex].15=\frac{.75}{1gal+V_2}[/tex]

    Hope this helped. Good luck.
     
  5. Sep 6, 2004 #4
    [tex]15\%(1gal+V_2)=75\%(1gal)+0\%V_2[/tex]



    It clears things up, but what is [tex] c_2 [/tex] ?
    Thanks
     
  6. Sep 6, 2004 #5
    C2 is 0% because pure water has 0% alcohol.
     
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