Convert 60 percent solution to 8 percent? - Answers

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!