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Math Help - Acid mixture question

  1. #1
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    Acid mixture question

    One solution is 10% acid and another is 22% acid. How many cubic centimeters of each should be mixed to obtain 100 cubic centimeters of a solution that is 12% acid?
    Last edited by mr fantastic; May 2nd 2009 at 04:06 AM. Reason: Moved from another thread
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  2. #2
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    Verify solution anyone?

    Quote Originally Posted by needhelp1 View Post
    One solution is 10% acid and another is 22% acid. How many cubic centimeters of each should be mixed to obtain 100 cubic centimeters of a solution that is 12% acid?
    In future, please post new questions as new threads, so they won't be so likely to be overlooked. Thank you!

    To learn, in general, how to set up and solve this sort of exercise, try here. Then:

    . . .cc's solution:
    . . . . .10%: x
    . . . . .22%: 100 - x
    . . . . .mix: 100

    . . .percent acid:
    . . . . .10%: 0.1
    . . . . .22%: 0.22
    . . . . .mix: 0.12

    . . .cc's acid:
    . . . . .10%: 0.1(x)
    . . . . .22%: 0.22(100 - x)
    . . . . .mix: 0.12(100)

    Add the inputs, set equal to the output, and solve for the variable.
    Last edited by mr fantastic; May 2nd 2009 at 04:08 AM. Reason: No edit - just flagging this reply as having been moved form a thread containing a duplicate question
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  3. #3
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    Quote Originally Posted by needhelp1 View Post
    One solution is 10% acid and another is 22% acid. How many cubic centimeters of each should be mixed to obtain 100 cubic centimeters of a solution that is 12% acid?



    The answer to this problem 10?
    The answer is two numbers the quantities of each of the two solutions that go into the mixture, if you gave some idea of the work or thinking that went into your suggested answer it would be easier for us to spot what difficulties you are having with this problem.

    Let the volume in cc of solution 1 be x, and of solution 2 be y. Then as we have 100cc of mixture:

    x+y=100.

    x cc of solution 1 contains 0.1x cc of acid, y cc of solution 2 contains 0.22y cc of acid, so the 100 cc of mixture contains 0.11x+0.22y, and this is 12% of 100 cc so:

    0.11x+0.22y=12

    So you need to solve these equations for x and y to get the required answer.

    CB
    Last edited by mr fantastic; May 2nd 2009 at 04:01 AM. Reason: No edit - just flagging this reply as having been moved from a thrread containing a duplicate question.
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  4. #4
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    Lets say we mixed "a" cc of 10% soln and "b" cc of 22%soln

    Amount of acid in First = 10a/100 = a/10

    Amount of acid in second = 22b/100

    Now its given that
    Total amount of mixture

    a+b = 100

    Amount of acid in mixture

    a/10 +22b/100 = 12

    Solve the two equations.
    solve the two equations!
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  5. #5
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    Hello, needhelp1!

    Another approach . . .


    One solution is 10% acid and another is 22% acid.
    How many cc's of each should be mixed to obtain 100 cc's of a solution that is 12% acid?

    Let x = amount of solution A (10% acid).
    Let 100-x = amount of solution B (22% acid).


    x cc's of A is 10% acid.
    . . It contains: 0.10x cc's of acid.

    100-x cc's of B is 22% acid.
    . . It contains: 0.22(100-x) cc's of acid.

    The mixture contains: {\color{blue}0.10x + 0.22(100-x)} cc's of acid.


    The mixture is 100 cc's which is 12% acid.
    . . It contains: 0.12(100) = {\color{blue}12} cc's of acid.


    We just described the final amount of acid in two ways.


    There is our equation . . . \boxed{\;0.10x + 0.22(100-x) \:=\:12\;}


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~


    The information can be organized in a chart . . .

    . \begin{array}{|c|| c|c|c|}\hline<br />
& \text{Sol'n} & \text{Percent} & \text{Acid} \\ \hline \hline<br />
A & x & 10\% & 0.10x \\ \hline<br />
B & 100-x & 22\% & 0.22(100-x) \\ \hline \hline<br />
\text{Mix} & 100 & 12\% & 0.12(100) \\ \hline \end{array}


    And the equation is waiting for us in the last column . . .

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  6. #6
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    Alright, I give up.

    I already have all that information. 10 is what I got so Im obvously no where near right.
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  7. #7
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    Quote Originally Posted by needhelp1 View Post
    One solution is 10% acid and another is 22% acid. How many cubic centimeters of each should be mixed to obtain 100 cubic centimeters of a solution that is 12% acid?
    Thread closed and user banned for sending an insulting pm.
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