I have nicotine which is 100mg 50/50 from a friend and would like to know what the equation is to add to make this 120ml a 6mg.
This is why we did all those word-problems back in math class. Turn your question into an equation you can solve:
"aalmosawi has 120ml of 3mg liquid. How many ml's of 100mg/ml should he add so that the resulting mixture is 6mg/ml?"
How many ml's ("x") must we add, so that the resulting mixture ("X + 120" ml's, and "100x + 3*120" total nicotine) is 6mg/ml (6 * [x + 120]). Let's work it out, shall we? You're going to add "x" amount of 100mg nicotine (total "x * 100" mg's of nic) to your 120ml bottle of 3mg (3* 120 = 360mg of nic, total.) So the amount of nicotine you have, when all is said and done, will be "360 + 100x". So let's start with that:
360 + 100x
That's how much nicotine you have, after you add "some amount" of 100mg liquid. How much nicotine do we want that to be? Well, we know that we will end up with "120 + x" ml's of liquid, and we want there to be 6mg of nicotine for every one of those 120+x ml's, so the total nicotine should be "6 * (120+x)"
So we know that the total amount of nicotine should be "6 * (120+x)". But wait, we also know that the total amount of nicotine should be "360 + 100x". So we have two different ways of representing the same total amount we're after, and both of them in terms of the same unknown variable "x". You know what that means, right? The two are "equal" to each other. Let's write that out:
360 + 100x = 6 * (120 + x)
Hey, that's great. Now that we have an equation, we can just solve for "x" with basic algebra:
100x + 360 = 6x + 720
100x + 360
- 360 = 6x + 720
- 360
100x = 6x + 360
100x
- 6x = 6x
- 6x + 360
94x = 360
94x
/ 94 = 360
/ 94
x = 360/94 or approximately 3.8297872...
So you should add about 3.8ml of your 100mg nic. Let's check:
3.8ml of 100mg nic is 380mg. Added to the 360 that were already in the bottle, that's 740mg of nicotine, in total. Adding 3.8ml to your 120ml bottle, you have 123.8ml in total. 740mg in 123.8ml is a concentration of 740/123.8 or 5.9773828... or very close to exactly six mg/ml.
