Math help

[Mezrein]

Hi all. I have a math question for everyone. When I create my all day juice mix it's 12.5 mil of 50/50 pg/vg 60mg strength juice, reduced by a 31.5 mil mix of 65/35 pg/vg then adding 6 mil of flavor. I need to know what the resulting ration of pg/vg is, as well as the formula used to get that ration so I can vary the ration of the reducer.
Challenge accepted?


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[MorpheusPA]

12.5 ml of your nic solution at 50/50 = 6.25 ml of PG, 6.25 ml of VG.

There's actually some nicotine in there, but it only throws the answer by 6%, or not enough to really matter here--3% error on each dilutant, or a bit over 0.18 ml. No big deal.

31.5 ml of 65 PG/35 VG = 20.48 ml of PG, 11.02 ml of VG.

20.48+6.25 ml of PG = 26.73 ml of PG
11.02+6.25 ml of VG = 17.27 ml of VG

You didn't specify if the 6 ml of flavoring was PG, VG, PGA, or alcohol based, but I'll assume PG for the sake of argument.

26.73+6 ml of PG = 32.73 ml of PG

Again, the actual flavoring throws the answer a little bit on the PG, but it's an unknown so I'll just ignore it.

32.73+17.27 ml = 50 ml total (as you already know)

32.73/50 = 65% PG
1-0.65 = 35% VG

The equation is obvious and left as an exercise to the reader.

Just kidding. I hated it when my books did that and the answer wasn't actually obvious.

PG = ((nic * 0.5) + (mix * 0.65) + (Flavoring amount)) / ((nic * 0.5) + (mix * 0.65) + (Flavoring amount) + (mix * 0.35))
VG = 1 - PG

 

[Vicshalls]

12.5 ml of your nic solution at 50/50 = 6.25 ml of PG, 6.25 ml of VG.

There's actually some nicotine in there, but it only throws the answer by 6%, or not enough to really matter here--3% error on each dilutant, or a bit over 0.18 ml. No big deal.

31.5 ml of 65 PG/35 VG = 20.48 ml of PG, 11.02 ml of VG.

20.48+6.25 ml of PG = 26.73 ml of PG
11.02+6.25 ml of VG = 17.27 ml of VG

You didn't specify if the 6 ml of flavoring was PG, VG, PGA, or alcohol based, but I'll assume PG for the sake of argument.

26.73+6 ml of PG = 32.73 ml of PG

Again, the actual flavoring throws the answer a little bit on the PG, but it's an unknown so I'll just ignore it.

32.73+17.27 ml = 50 ml total (as you already know)

32.73/50 = 65% PG
1-0.65 = 35% VG

The equation is obvious and left as an exercise to the reader.

Just kidding. I hated it when my books did that and the answer wasn't actually obvious.

PG = ((nic * 0.5) + (mix * 0.65) + (Flavoring amount)) / ((nic * 0.5) + (mix * 0.65) + (Flavoring amount) + (mix * 0.35))
VG = 1 - PG

OMG! my brain hurts just looking at that. Math! Yuck!

 

[Train2]

I'd convert this to a "standard" recipe format - then you can use a calculator to play with it easily.
Here's what you're making, as you'd enter it in the EJuiceMeUp calculator (which I highly recommend):

Nicotine Strength e-Juice PG 50% VG 50% 60mg
Target Nicotine Strength 15mg
Amount to Make 50ml

Nicotine eJuice 12.5ml 25%
PG 50% 12.75ml 25.5%
VG 50% 18.75ml 37.5%
Flavor 6ml 12%

Using the calculator let's you avoid the math errors that can easily be made - for instance, if you want to lower the nicotine, it also changes the PG/VG ratio. If you add another flavor, it changes ALL the percentages!

The ONLY thing the calculator doesn't automatically handle is that you're adding your no-nic PG/VG by using a pre-mix at 65/35. You can either deal with that math manually, or do them separately in the future...

Hope that helps a little!!

 

[MorpheusPA]

Looking at this, yes, it makes the head hurt just a wee bit, doesn't it?

We can help out with that by using a variable:

X = (nic * 0.5) + (mix * 0.65) + (Flavoring amount)

PG = X / (X + (mix * 0.35))
VG = 1 - PG

 

[Mezrein]

Ya my head imploded a bit there but inthink I get the idea. Thank you much all!


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