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March 14th, 2017, 07:42 PM   #1
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Question I'm stumped! Mixing Liquid Concentrates

This SHOULD be easy, but I don't know why I can't solve it. I've tried Excel and still can't do it. I've spent countless hours on this and am stumped!

Suppose the concentrates below are all different chemicals. They also have the same consistency as water and can be used together to dilute each other with no additional water needed.

Each concentrate below has its own bottle because they are a DIFFERENT type of chemical from each other. The label on each specifies an amount of liquid that MUST be diluted to a specific ratio of another liquid. Water can be added if needed as long as they're diluted to the ratio.

Liguid Concentrate to Liquid ratio:

c1 needs 1:2 (one part liquid concentrate, 2 parts liquid (i.e. water or another concentrate)
c2 needs 1:3
c3 needs 1:4
c4 needs 1:8

PROBLEM:

I need a MIXTURE of all the above concentrates that will fill a 1000ml vessel. The original dilution ratios MUST still be preserved for EACH concentrate in the final mixture.

I thought this would be as simple as adding fractions I just don't know why my mind can't figure it out.

Thanks for any help; it's REALLY appreciated!

Last edited by skipjack; March 14th, 2017 at 11:28 PM.
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March 14th, 2017, 11:42 PM   #2
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For, say, c2, the volume of c2 must be 250ml so that the remaining 750ml of other liquids gives the desired 1:3 ratio for the c2.

Similarly, the volume of c3 must be 200ml.

Adding the volumes for all four concentrates gives a total that is less than 1000ml, so the rest of the 1000ml is water.
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March 14th, 2017, 11:55 PM   #3
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ok.. Suppose we have volume $V$

$c1 = \dfrac{V}{3}$

$c2 = \dfrac{V}{4}$

$c3 = \dfrac{V}{5}$

$c4 = \dfrac{V}{9}$

$c1 + c2 + c3 + c4 = V \dfrac {161}{180}$

Now... let's add $\dfrac {19V}{180}$ of water

now the concentrations add to 1 and we simply multiply by $V=1000$ to get the amounts (in ml)

$c1 = 333 ~ \dfrac 1 3$

$c2 = 250$

$c3 = 200$

$c4 = 111 ~\dfrac 1 9$

$water = 105 ~\dfrac 5 9$

You can check that the concentration ratios are all correct and that these amount sum to 1000 ml.
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