Question

how much of a 1:5 stock supply you need to make 600mL of 1:12 boric acid solution

Answer 1

So X amount of a 1/5th conc of pure stock solution ='s 600ml of 1/12th concentrated working solution. Welcome to my daily grad school math! (Not one calculus problem- oh the waste! :-) )

So think of this as a ratio problem. The two sides stock = final must stay equal. Another-words:
X ml of stock * (0.2 conc Stock solution) = 600ml final * (0.08333 conc of Final Solution)
My concentration on the left is higher that the concentration of the solution on the left. So it will take less than 600ml of stock to have the same number of molecules (amount) of chemical is produced by the two numbers on the right side of the equation.
Divide both sides by 0.2 conc ...
X = 250 ml of the 20% Stock Boric Acid Solution and adding the rest of the solvent (water?) to acheive the final 600 ml of Boric Acid solution.
This can be done with the fractions but some may recommend converting to percentages as a practice.
\[\frac{1}{5}*X\space ml = \frac{1}{12}*600\space ml\space Final\space Boric \space Acid\]
\[X = \frac {5}{1}*\frac{1}{12}*600\space ml=\frac{5}{2}*100\space ml=250 \space ml\space of \space stock \space BA \space\]