Convert 60 percent solution to 8 percent?
Answer: Take whatever volume of 60 percent solution you have,
multiply that volume by 52 and then divide that amount by 8, this
is how much water to add to get an 8% solution. ( or multiply by 13
and divide it in half, this is the same thing) Answer explained
below. Think of 3 jars. The first has 60% solution, the next has
just water, the third has 8% solution. So we want to know how much
water to add. Now we need some equations. 60% solution is 60 units
of something, and say we have a volume V of it. So the amount stuff
in V is .6V. Just to clarify, the total volume of 60% liquid is V
and let's say it is salt water. Then we have 60% of it is salt and
the actual amount of salt we have is .6v. Now we are adding to the
volume, but not adding salt. We add x liters to V so our total
volume we add to get 8% is V+x. Now the 8% has (we use salt just to
make this more concrete, but obviously cement would do the same or
acid..bla bla bla) So the quantity of salt in our final solutin is
.08(V+x), however, we only added water, so the amount of salt is
the same. That means .6V=.08(V+x) so this is our equation! multiply
by 100 to get rid of the decimals. We have 60V=8V+8x or 52V=8x so
x=52V/8 That means for any given volume of water, we multiply the
volume by 52 and divide by 8 to see how much water to add. Let's
try it! Say V=8 Liters. I pick that since it should make the 8's
cancel. So we have 8 liters of 60% salt solution. This mean we have
.6(8) grams of salt, or 4.8 grams. Now we add 52 x/8 or 52 liters
of water. Our total volume now is 52+8=60 liters and we did not add
salt so we still have 4.8 grams. What percent solution is this? 4.8
grams/60 is .08% as desired so it works!