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Math Help - Reverse ratios and percentages....

  1. #1
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    Reverse ratios and percentages....

    The teachers were right.... we will need this one day!!! I didn't do so well in math class. Thank you for forums like this!

    I am working with dilutions of a concentrate. (I will give both gallons and lbs.)

    We have a diluted drum of 55 gallons/450lbs. Of that, 15 Gal/122.715 lbs is the concentrate. 40 Gal/327.285 lbs is the water. I think that is a 3:8 dilution ratio. When performing a solids/activity test on this diluted product, we find the finished drum has 11.65% solids/activity. We do not have the original concentrate and need to determine what the solids/activity of the original concentrate is.

    (I hope someone will tell me it is as simple as multiplying 11.56 by 3)

    On the flip side...... We often have a concentrate for which we know the % of solids/activity ie. 49%. Then I want to plug into a formula (which I don't have) to determine the resulting solids at a known ratio ie. 1:75, or 1:120 etc....

    Again I hope I'm making this too complicated and there is some very simple formula that I missed that day I skipped class to go swimming!


    humbly in appreciation.
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  2. #2
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    Re: Reverse ratios and percentages....

    Hey lisach.

    Percentages are basically some ratio times 100%. So if your ratio is say 1/10 = 0.1 then the percentage is 1/10 * 100% = 0.1 * 100% = 10%.

    With regards to the dilution you calculate 15/40 = 3/8 just as you have done so yourself. Remember its just a ratio of one thing relative to another (in this case, concentrate relative to water).

    To convert that to a percentage we multiply that ratio by 100% which gives us 3/8 *100 = 300/8 = 75/2 = 32.5%
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  3. #3
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    Re: Reverse ratios and percentages....

    Ok... Well that is the first step. I get so lost here ..... Yes the ratio of the finial diluted drum is 3:8 and the percentage of concentrate in the drum is 32.5%, that is part of what I need but all of it. Let me go here for a minute....On the reverse side.
    • A concentrated sugar solution that is 49% sugar and 51% water has 49% activity/solids in it.
    • I dilute it with water at 1:75 ratio to make 450lbs/55 Gal. The drum then has 76 parts. 55 Gal=7040 oz---- 7040 oz/76=92.63 oz---- 1 part = 92.63 oz.
    • If 1 part is the original concentrate, and it is 49% active then 92.63oz*49%=45.389 oz. So if the sugar was all condensed in a little packet sitting in the bottom of the drum it would be 45.389 oz in 7040 oz.
    • 45.389/7040= 0.645%
    • Therefore, if a concentrate with 49% activity diluted at 1:75 ratio will have an activity of .645% as a final dilution activity.
    Please correct me at this point if I am wrong....

    If I was using a formula to get this instead of drawing out visual representations, I would be able to plug in the known factors and figure the reverse.
    a) activity level of concentrate 49%
    b) dilution rate 1:75
    c) volume of diluted product 55 Gal
    d) activity level of diluted product .645%

    A final diluted drum of 55 Gal that was diluted at 3:8 ratio has an activity of 11.65%.
    How do we determine what the percentage activity of the original concentrate was.

    (like a deer in headlights here.....)
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  4. #4
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    Re: Reverse ratios and percentages....

    drum contains 450 lbs of diluted concentrate
    assay of drum= 11.56% solids
    solids in drum=0.1156 * 450 = 52 lbs
    solids in concentrate =52/122.7=0.424 fraction 42.4%
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  5. #5
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    Re: Reverse ratios and percentages....

    Ok... That looks very good..... Now to expand on that further......

    a=activity of concentrate c=volume of diluted product
    b=dilution rate d=activity of diluted product
    Is there a quick way to determine the following?
    1. Unknown activity level of final diluted product X
    a=49% b=1:75 c=450lbs d=x

    1. Unknown dilution rate X
    a=49% b=X c=450lbs d=12%
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  6. #6
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    Re: Reverse ratios and percentages....

    I assumed that activity was % solids.If you need to make dilutions based on solids content or some other concentration unit I can help but you must clearly define what you want.
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  7. #7
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    Re: Reverse ratios and percentages....

    yes activity is the same thing as % solids
    I'm not sure what else to clarify
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  8. #8
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    Re: Reverse ratios and percentages....

    given concentrate 49% solids
    specific gravity not given.I will assume 1.5
    dilution rate by volume 1:75
    1gal conc = 8.35* 1.5 * 0.49 = 6.14 lb solids
    75 gal water = 8.35 * 75=626.4 lbs water
    Total wt of mix =632.4 lbs
    % solids = 6.14 / 632.4 *100=0.97% by wt
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