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Math Help - Percentage problem

  1. #1
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    Percentage problem

    A 100 liter barrel of vinegar is 8% acetic acid. Before it can be bottled and used in cooking, the acidity must be reduced to 5% by diluting it with pure water. In order to produce 64 liters of usable vinegar, how many liters of vinegar from the barrel and how many liters of pure water should be combined?

    I am doing guessing and checking right now but could someone show me how to make an equation to get the answer?


    8/100

    4/ 50+X = 1/20

    2/ 25+X= 1/20


    I am trying to get to 64 liters and i am sure there must be a better way to get to the anwer.

    Thanks

    Vicky.
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  2. #2
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    Quote Originally Posted by Vicky1997 View Post
    A 100 liter barrel of vinegar is 8% acetic acid. Before it can be bottled and used in cooking, the acidity must be reduced to 5% by diluting it with pure water. In order to produce 64 liters of usable vinegar, how many liters of vinegar from the barrel and how many liters of pure water should be combined?
    let x = liters of 8% acid

    y = liters of water

    x + y = 64

    x(.08) + y(0) = 64(.05)

    solve the system
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  3. #3
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    If the solution of your vinegar is 8%, what is the other 92% composed of?
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  4. #4
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    Quote Originally Posted by skeeter View Post
    let x = liters of 8% acid

    y = liters of water

    x + y = 64

    x(.08) + y(0) = 64(.05)

    solve the system


    Thanks for your help but I didn't understand the solution enough to use it
    so I had to keep on guessing and checking until I got

    3.2/ 40+X = 1/20 X= 24

    Thanks.

    Vicky.
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  5. #5
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    Quote Originally Posted by Vicky1997 View Post
    Thanks for your help but I didn't understand the solution enough to use it
    so I had to keep on guessing and checking until I got

    3.2/ 40+X = 1/20 X= 24

    Thanks.

    Vicky.
    What his equation (or system of equations) was saying is that:

    X is total amount of ACID you have.

    Y is total amount of WATER you have.

    64 is the total amount of VINEGAR you have (as vinegar is made up of, well whatever it is made of and water).

    From the barrel you currently have, there is 8/100 parts of ACID and 92/100 parts of water, for a total of 100/100 part of VINEGAR.

    You need to figure out how much of the current solution to take, and how much of new water to make a VINEGAR solution that is 5/100 ACID and 95/100 WATER.

    Does this help at all? No guessing allowed.
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