Math help

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Izan

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zoiDman

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Ahhh excellent, thank you guys so much! That math is soo much easier. :) Now, lets say I wanted to bring that 90ml of 8mg strength up to 12, I have 60mg base liquid, how much do I need to add to the 8 to get it to 12? :) You guys are awesome, :)

Milligrams per Milliliters is the Ratio of Total Milligrams divided by Total Milliliters.

ie: (Total mg) / (Total ml) = mg/ml

Let's call "X" the Amount in ml you will add of the 60mg/ml to your existing 8mg/ml e-liquid.

So the Total Nicotine of what we will add will be 60mg times X. Or just 60X of Total Nicotine.

And, 90ml of 8mg/ml = 720mg of Total Nicotine.

Now lets plug this into our Total Milligrams divided by Total Milliliters formula.

=>
(720 mg + 60X mg) / (90ml + X) = 12mg/ml

We can drop the mg's and ml's because they are just telling us what each value represent. And we are Solving for X which represents the amount of ml's of 60mg/ml to be added.

=>
(720 + 60X) / (90 + X) = 12


Now lets Multiple both side by (90 + X) to get ride of that Pesky Fraction.

=>
(720 + 60X) = 12(90 + X)

Now lets Slam Out some terms on the Right Hand side and Drop the Parentheses.

=>
720 + 60X = 1080 + 12X

Now lets Collect everyone who is alike and put them on one side of the Equal Sign

=>
60X - 12X = 1080 - 720

Now Turn the Wrench.

=>
48X = 360

Turn the Wrench again.

=>
X = 360 / 48


Once More

=>
X = 7.5

So it sounds like we need to Add 7.5ml of 60mg/ml to 90ml of 8mg/ml to Obtain 97.5ml of 12mg/ml.

Cool. It's Miller Time! Done Right?

No. Always Double Check.

Plugging things back into out mg/ml Formula ...

((90 x 8) + (7.5 x 60)) / (90 + 7.5) = 12

1170 / 97.5 = 12

And Bingo. It Jives!

---

So when doing one of these How Much should Add problems, the Key is understanding that mg/ml = Total Nicotine / Total Milliliters.

Something that I Think would be Easier for people to Visualize if we wrote everything as Bla Bla mg/ml. Instead of Bla Bla mg.

BTW - Someone should Check my Typing/Math. Because I wrote this while only on 1 Cup of Coffee.
 

zoiDman

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My brain just broke.. I havent done long math like that since I was in high school and we're not going to talk about how long ago that was. But if verified, I owe everyone miller. :)

Trust Me. It looks a Lot Worse than it really is.

And even a Relatively straight forward Math problem looks like Rocket Science when someone writes All the steps down in it's Full Algebraic Glory.

:D
 

Katdarling

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zoiD!!! LOL! You're amazing, but I have NO KLUE what that problem solving and resulting answer was all about!

I take the path of LEAST resistance and use what Izan likes as well, the ejuicemeup calculator. The only thing is.... ya gots ta play with the numbers to get there.

The only number (@Mezrein) that needs to be adjusted is the highlighted one (the amount of Nic Base 2 - your 60mg).



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zoiDman

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zoiD!!! LOL! You're amazing, but I have NO KLUE what that problem solving and resulting answer was all about!

...

No Worries Kat.

Post #6 is just what Retired Mathematics Instructors do for Fun. LOL.

:)
 

Hawise

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No Worries Kat.

Post #6 is just what Retired Mathematics Instructors do for Fun. LOL.

:)

Not a math instructor, but I amused myself by working out the formula for how much nic base to add in much the same way.

X = nicotine base to add

(initial volume) * (initial concentration) + (base concentration) * (X) = (target concentration) * (initial volume + X)

solving for X you get

X = [ (initial volume) * (target concentration - initial concentration)] / (base concentration - target concentration)

= [ 90 ml * (12 mg/ml - 8 mg/ml)] / (60 mg/ml - 12 mg/ml)

= (90 ml * 4 mg/ml) / 48 mg/ml

= 360 mg / 48 mg/ml

= 7.5 ml

Even the units work out, as they should. And there's proof algebra is useful!
 

zoiDman

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Not a math instructor, but I amused myself by working out the formula for how much nic base to add in much the same way.

X = nicotine base to add

(initial volume) * (initial concentration) + (base concentration) * (X) = (target concentration) * (initial volume + X)

solving for X you get

X = [ (initial volume) * (target concentration - initial concentration)] / (base concentration - target concentration)

= [ 90 ml * (12 mg/ml - 8 mg/ml)] / (60 mg/ml - 12 mg/ml)

= (90 ml * 4 mg/ml) / 48 mg/ml

= 360 mg / 48 mg/ml

= 7.5 ml

Even the units work out, as they should. And there's proof algebra is useful!

Yeah... Lots of ways sometimes to get from Point "IC" to Point "TC" metaphorically speaking.
 

dyanaprajna

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Math was always my favorite subject in school-I even graduated high school with 6 advanced maths. While other people were filling electives with easy/fun classes, I took more math (and science classes). And my father-in-law, after he got out of Korea, taught math (he has a degree in it), to prisoners at the local prison for 30 years. So since math runs in my family's blood, why is my daughter having such a hard time with it? :p. Seriously though, I love math and numbers, and this post made my day. :)
 

zoiDman

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Math was always my favorite subject in school-I even graduated high school with 6 advanced maths. While other people were filling electives with easy/fun classes, I took more math (and science classes). And my father-in-law, after he got out of Korea, taught math (he has a degree in it), to prisoners at the local prison for 30 years. So since math runs in my family's blood, why is my daughter having such a hard time with it? :p. Seriously though, I love math and numbers, and this post made my day. :)

My Dad was an Engineer. And my Mom has a Degree in Applied Mathematics and Masters in Accounting.

My Sister was a HS Spelling Bee Champion. And can Tell you when a Conjugated somethingorother modifies a Interrogative Pronoun. But struggles with Higher Math concepts.

Me. I pegged the Math Achievement Tests in HS. And went on to get a Degree and somehow fell into Teching Math at a College. But I speel like a thurd grader.

The Family Joke is that I somehow got all the Numbers. And my Sister got all the Letters.

LOL
 
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