If I have 3 glucose control solutions having:
Low - 50 mg/dl
Normal - 100 mg/dl
High - 330 mg/dl

I want to calibrate a glucose meter but I need more than these 3 data points. How can I mix these up to get different concentrations in between 50 and 100, 100 and 330. I would like to mix up different concentrations and put them in test tubes or whatever to do some calibration work. Like 70 mg/dl, 90 mg/dl, etc. More data points should be in between say 50 and 100 since this is normal, 90 mg/dl is considered close to normal.
question is:
secondary (10-12)


Hi John.

You can create any concentration you need in whatever quantity you desire by using "simultaneous linear equations", which is a fancy term for algebra you probably already know.

Let's say you have lots of 50 mg/dl and 150 mg/dl solutions and want 1dl of concentration C (mg/dl). Let's call the quantity of the low concentration L and the other one H.

Then 50 mg/dl x L dl + 150 mg/dl x H dl = C mg

As well, since you want 1 dl in total, L dl + H dl = 1 dl

Mathematically, that is:

50L + 150H = C,
L + H = 1

If you rearrange the bottom equation to solve for L, you get L = 1 - H, which you can substitute for L in the previous equation:

50(1-H) + 150H = C

which reduces to 50 + (150-50)H = C.

Now you can choose C (say 80 mg/dl) and use this formula to find the amount of 150 mg/dl (high concentration) solution to start with. Then you just fill the container up to the 1 dl mark with the 50 mg/dl (low concentration) solution.

You can set this up using any concentrations you have lots of - even odd ones you concoct in earlier mixing (for example, how much 82 mg/dl solution and how much 119 mg/dl solution do you mix to get 1 dl of 109 mg/dl solution?)

Hope this helps,
Stephen La Rocque.