Calling all mathmeticians/ chemists!

[Squirt's Mom]

Your assignment -

There are 16 oz net weight (473 ml) of 95% glycerine / 5% water and the full 16 oz must be used. To this 16 oz - water and Brandy need to be added. The Brandy is 40% alcohol and 60% water by volume.

The finished solution needs to be 75% glycerine, 15% water, and 10% alcohol.

How much water and how much Brandy should be added to the 16 oz of glycerine to achieve that final solution?

:p

[lulusmom]

Sorry but moving on to next thread. :o

[molly muffin]

Glynda wait up!! I'm right behind you!! Don't leave me here with Math!!

[mcdavis]

Well I got as far as putting the data onto an xl sheet and staring at it......... then remembering that I never really got percentages :confused:

[molly muffin]

Grabbing MC's hand and pulling her out into the sunlight. Don't go to the dark side!!

I might be having too much fun with this Leslie! And not an answer in sight either!

[mytil]

Interesting Leslie. I am with MC :) - put it into a spreadsheet and actually trying the ratio bit and I am guessing that the alcohol will dilute the glycerine so will let you know. :)

[Squirt's Mom]

:p:D:p:D Glynda, Sharlene, MC! :D:p:D:p I just knew someone here would know how to formulate this! :D

I keep wanting to add 1.6 fluid oz of each but when you work it backwards, that doesn't come out right. Then I came up with 1.9 oz of each that somehow works backwards closer. A doc friend I asked said 2 oz of each....but I got the distinct impression he was simply telling me that to end the debate of allopathic VS Holistic medicine...which he was not winning. :D

So ya'll keep on trucking with this - those of you still in the dark anyway! :p The truth is out there (per Moulder anyway!). :p

[lulusmom]

My brother is a mathematic wizard so I asked him if he knew the answer and his response was:


No, because I would never ever screw up an 80 proof brandy by mixing any thing with it.

I tend to agree with him. :D

[Squirt's Mom]

Lmao :d:d:d

[molly muffin]

Okay I emailed the question to my husband, my math wiz, who is partial more to a single malt scotch, so hoping he won't take exception to messing with a good brandy. hahahahaha

We'll see.

I'm still in the light!
Sharlene and molly muffin (she doesn't do math either)

[molly muffin]

Email back from the hubs, saying it should be easy enough. (pffftttt) and that he will solve it when he comes home this evening.

We shall see how easy it is, but I'm sure he'll have something for us. LOL I'm pouring him a scotch when he walks in the door just in case. No sense tempting fate by offering a brandy!!

[Trish]

Your assignment -

There are 16 oz net weight (473 ml) of 95% glycerine / 5% water and the full 16 oz must be used. To this 16 oz - water and Brandy need to be added. The Brandy is 40% alcohol and 60% water by volume.

The finished solution needs to be 75% glycerine, 15% water, and 10% alcohol.

How much water and how much Brandy should be added to the 16 oz of glycerine to achieve that final solution?

:p



First part = 24ml water + 449 ml (rounded to 450) glycerine total 473ml

Each 100ml of your brandy/water mix = 40ml brandy + 60ml water

So if the 450 ml glycerine needs to be 75% of the mixture you need a TOTAL VOLUME of 600ml

To that leaves 150ml to add to our glycerine.

Now the concentration in the brandy is 40% actual brandy. So 150ml of your brandy mix gives 60ml of straight brandy which is exactly the required amount of 10% alcohol.

Finally water = we have 24ml in the initial glycerine/water mix. + the rest of the water portion in the 150ml brandy/water mix = 90ml

So finally, my calculations ... my brain is hurting at this point...

473ml (16oz) glycerine/water mix
Made up of 24 ml water + 449ml glycerine (75% total glycering)

Add 150 ml Brandy/water
Equals 60ml brandy being 40% of that volume (10% total alcohol)

Water 24 (from original glycerine mix + 90ml from brandy/water mix) = 114ml which is 19% of our total volume :mad:. But with the ingredients we have to work with that cannot be altered without you going and buying 100% alcohol. Is the glycerine/water mix already made up? Because if you could leave out the 24ml of water in that it would be perfect!!! ie the 90ml water from the brandy mix would be a neat 15% total water!!

So ideally, it should be
450ml Straight glycerine 75% (no water)
150ml Brandy/water mix, made up of 60ml brandy 10% and 90ml water 15%

Best I can do Leslie, I guess if cannot change the glycerine/water mix then the total water in finished product will only be slightly over, maybe ok??

[molly muffin]

Hubby would like clarification on a point.


Are you sure about the particulars? The glycerine require dictates that a set amount of dilution of the base solution is required, yet at that dilution it may not be possible to achieve the desired alcohol content

He is waiting on his jeep work, so guess he decided to go forward and take a look at the problem.

Sharlene

[labblab]

OK, am I gonna be the first one to ask -- what the heck is this brandy solution gonna be used for??? :confused: :eek:

(I'd rather drink my brandy neat, thank you very much! ;) :p)

[Squirt's Mom]

uhhhh....huh?

If he is asking am I sure water has to be added, no I'm not. The water content of the brandy may suffice. The 16 oz of glycerine is 95% glycerine and 5% water.

[Squirt's Mom]

LOL Marianne - it's actually a glycerine solution with a little bit of brandy added. I will be making glycerites with it. The brandy will pull a tiny bit more of the constituents out of the herb plus add shelf life to the finished product without having the harsh taste or effect of an alcohol tincture.

[Squirt's Mom]

Tracy, I have no idea where the answer is in all that! :p But the 16 oz of glycerine is fixed and the whole 16 oz must be used. So that is the only known. The 16 oz is 5% water and 95% glycerine.

[molly muffin]

I just copy/pasted your answer Leslie and Trish's possible solution on to hubs.

[molly muffin]

This might be driving us TO the brandy!

[mytil]

Awww was going to try and calculate it tonight when I had the time...good job Trish!

I agree, straight up with Brandy. (BTW, what type of Brandy?)
This could influence the mixture. ;)

[Squirt's Mom]

Jump on in Terry! I have no idea what Tracy's answer is! :D I don't see anything that says - "add X water and X brandy". :p

[molly muffin]

From Molly Muffins dad:

The answer is somewhere around 126.1333 ml and 149.7833 ml of brandy added to the glycerine solution. No additional water is required.

When in doubt, drink more brandy.

The solution A is a total volume of 473 ml. Of that 449.35 ml is glycerine and 23.65 ml is water.

Running balances:
Glycerine 449.35 ml
Water. 23.65 ml
Alcohol. 0.0. ml

In order for 449.35 to be 75% of a total volume, that total volume must be 599.1333 ml

449.35 / .75 = 599.1333

Since our total volume will be 599.1333 and we wish 10% to be alcohol, we need 59.9133 ml of alcohol.

599.1333 * .10 = 59.9133

The amount of Brandy required to provide 59.9133 ml of alcohol is 149.7833 ml.

59.9133 / .4 = 149.7833

Yes, that is a problem as that will bring our total solution up by 23.65 ml too much. Since our glycerine is a constant, we know that we will be less than 75% glycerine. But let's carry on.

That amount of brandy also provides 89.87 ml of water

149.7833 * .6 = 89.87

Running balances

Glycerine 449.35 ml
Water. 23.65 ml + 89.87 ml = 113.52 ml
Alcohol. 59.9133 ml
Total volume 473 ml solution A + 149.7833 ml brandy = 622.7833 ml.

Percentages
Glycerine 449.35 / 622.7833 = .7215 (72.15%)
Water. 113.52 / 622.7833 = .1822 (18.22%)
Alcohol. 59.9133 / 622.7833 = .0962 (9.62%)

Close, but we missed all targets by a bit. Let's see what it looks like if we impose a volume limit to ensure 75% for the glycerine, then we will limit the brandy to 126.1333 ml.

599.1333 ml (from way above) - 473 ml is solution A = 126.1333 ml.

That amount of brandy provides 50.4533 ml of alcohol

126.1333 * .4 = 50.4533

That amount of brandy also provides 75.68 ml of water

126.1333 * .6 = 75.68

Running balances

Glycerine 449.35 ml
Water. 23.65 ml + 75.68 ml = 99.33 ml
Alcohol. 50.4533 ml
Total volume 473 ml solution A + 126.1333 ml brandy = 599.1333 ml.

Percentages
Glycerine 449.35 / 599.1333 = .75 (75%)
Water. 99.33 / 599.1333 = .1657 (16.75%)
Alcohol. 50.4533 / 599.1333 = .8421 (8.42%)

Again, off by a bit on two targets, but that is the reality of it.

[Trish]

From Molly Muffins dad:

The answer is somewhere around 126.1333 ml and 149.7833 ml of brandy added to the glycerine solution. No additional water is required.

When in doubt, drink more brandy.

Running balances

Glycerine 449.35 ml
Water. 23.65 ml + 75.68 ml = 99.33 ml
Alcohol. 50.4533 ml
Total volume 473 ml solution A + 126.1333 ml brandy = 599.1333 ml.

Percentages
Glycerine 449.35 / 599.1333 = .75 (75%)
Water. 99.33 / 599.1333 = .1657 (16.75%)
Alcohol. 50.4533 / 599.1333 = .8421 (8.42%)

Again, off by a bit on two targets, but that is the reality of it.

I concur, pretty much what I got apart from me rounding it up slightly!!! If we could get that 5% of water out of the base mixture of 95% glycerine/5% water the equation would be perfect. But I doubt we can remove that 23ml of water to get it perfect.

Unless Leslie goes and buys 450ml pure glycerine with no water added and then add 150ml of brandy at its perfect... that darn 23ml H20 :mad:

[Squirt's Mom]

:D:cool::D:cool: YAY! Thanks Sharlene's hubby and Tracy! Now I can get to work! The lady who usually figures these things out for me is sick and unable to be online currently so I was LOST. I foolishly thought I could do it....HA! Then I got a different answer from everyone I asked but they were all saying to add the same amounts of water and brandy, which I knew wasn't right. So thank you all and I hope the headaches are over for you by now. ;)

[lulusmom]

I have my dunce cap on and will now go sit in the corner for a bit.

[molly muffin]

Glynda I am right there with you. I have Never like mathematics. Hubby thank goodness seems to thrive on it.
I'm sure you will do just find with what he and Trish came up with as their answers, completely independent of each other came out to be the same thing.

Good luck and herbal onwards!
sharlene and molly muffin