Question 823041
Add diluent to go from 10% to 8%...

400 grams of 10% solution,
Want 8%; how much water to add?


{{{10*r=8}}}
{{{r=8/10=highlight_green(4/5)}}}


{{{(400*grams*(10*grams*acid)/(100*grams*solution))*(4/5)=(8*grams*acid)/(100*grams*solution)}}}


You will note the 4 to 5 ratio of the 10% to the 8%, and the "4" part is for the 10% acid solution.  Think how this proportion would work.  The amount of mass of the solution will be {{{5/4}}} times the 400 grams of the 10% acid.  This means, 500 grams of the resulting 8% solution, an addition of 100 grams of water.



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THIS COULD ALSO BE DONE USING STRAIGHTFORWARD ALGEBRA to setup the proportions.  If you feel more comfortable this way, then you could use:
Let w = grams of water to add.


{{{highlight(400*10/(400+w)=8)}}}, fill in the units as fit if you need them,
'
{{{400*10=8(w+400)}}}
{{{400*10=8w+3200}}}
{{{8w=4000-3200}}}
{{{8w=800}}}
{{{highlight(w=100)}}}