Percent of concentration math

tcebob · 25 Jan 2018

Can't find in Google and hope someone can jog my memory.

I recall somewhere around the 7th or 8th grade trying to cope with percent concentration arithmetic. Example:

"How much 25% butterfat milk must I add to 1 gallon of 10% b.m. to produce 15% b.m.?"

Never quite got it -- but learned calculus and became an engineer anyway. Now, thinking about it, I still can't get it, and let me tell you, my butterfat milk is beginning to ripen. So can someone direct me to a method or give a solution?

cereberus · 26 Jan 2018

Here is how.

You add A gallons @ 25% to 1 gallon @ 10% to make A+1 gallons at 15%

Thus

A*0.25 + 1*0.1 = (A+1)*0.15

A*0.25 + 0.1 = A*0.15 + 0.15

rearranging and adding/subtracting

A*0.1 = 0.05

Hence A = 0.5

Check final concentration with 0.5@25% added to 1@10% with total volume of 1.5

(0.5*0.25+ 1*0.1)/1.5 = 0.225/1.5 = 0.45/3 = 0.15 ---> Check!

General formula

X + Y = Z

X*CX+ Y*CY= Z*CZ

X,Y,Z are volumes

CX,CY,CZ are volume fractions (%/100) of component being considered

So long as you know any four of the above, you can solve the above as you have two equations and two unknowns

In your case, you knew X was 1 and the three concentrations and hence could obtain Y and Z

tcebob · 26 Jan 2018

Thanks, Cereberus. I'll remember it now.