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Home Cosmetic Science Talk Formulating Can’t make this calculus :(

  • Can’t make this calculus :(

    Posted by pma on May 24, 2023 at 4:38 pm


    Each line is an ingredient…

    I need to add ingredients to batch 21 in order to achieve the same proportions of batch 22.

    But since I can’t remove anything, only add, I think it’s not possible to save batch 21 (achieve proportions of batch 22), right?

    I will explain better: I have batch 21. Bath 21 and 22, of course, have the same ingredients. But I need to transform batch 21 in order to achieve the same proportions of 22 for all ingredients.

    Can anyone help me?

    pma replied 3 days, 12 hours ago 4 Members · 6 Replies
  • 6 Replies
  • evchem2

    May 25, 2023 at 3:33 am

    Is it possible for you to dilute batch 21 (I would make the dilution based on the 3rd ingredient, you’d need to take ~41% of 21) with water and the other ingredients added back in sufficient quantity to reach the same % as 22?

  • Richard

    May 25, 2023 at 4:00 am

    Can you split Batch 21 into 3 equal part batches and then add each ingredient accordingly to the required amount so that you end up with 3 batches?

  • fareloz

    May 25, 2023 at 4:03 am

    If you can afford to make a second batch of the same weight and then mix them both together you could average the percentage to the required specs.

    Basically x = 11.4, y = 37.0, z = 38.0

  • pma

    May 25, 2023 at 7:28 am

    Hi Fareloz!

    Thank you so much for helping me!

    I see you’re right because the numbers are obviously working, but I’m not sure if I understood how you got the values for x, y and z (even with the fact I’m seeing the numbers are correct). Can you explain me a bit more?

    • fareloz

      May 25, 2023 at 7:41 am

      If we make a new batch of the same size and mix it with the original one we will have a double-size batch with averaged percentages. I mean if you take 1g of 10% solution and mix it with 1g 20% solution you will get 2 grams of (10+20)/2 = 15% solution.

      The equation is: (original + adjusting) / 2 = target

      We know original solution, we know target solution. We can mark adjusting solution as x (y,z, etc) and create an equation. Let’s make one for water (I guess it is the first ingredient):

      (64.4 + x) / 2 = 37.9

      You need to solve this equation and you will find the numbers:

      64.4 + x = 37.9 * 2

      x = 37.9 * 2 - 64.4 == target * 2 - original

  • pma

    May 25, 2023 at 6:44 pm

    Thank you again for your explanation, I understood perfectly now.