Question 201532: How many milligrams of pure water must be added to 6 mg of a 40% solution to obtain a 25% solution? Found 2 solutions by nerdybill, Theo:Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website! How many milligrams of pure water must be added to 6 mg of a 40% solution to obtain a 25% solution?
.
Let x = milligrams of water added
then
.40(6) = .25(6+x)
2.4 = 1.5 + .25x
0.9 = .25x
3.6 mg = x (amount of pure water)
You can put this solution on YOUR website! your solution is 6 grams.
.6 of that is water so you have 3.6 grams of water in the existing solution.
.4 of the solution is not water.
you have 2.4 grams of not water in the solution.
there are several ways of looking at this.
looking at the 2.4 grams that is not water and knowing that will remain the same, you can use that to determine the total solution.
it is currently .4 of the solution.
divide 2.4 by .4 and you get 6 grams which is the current solution.
divide 2.4 by .25 and you get 9.6 grams which will be the new solution since that solution will be .25 times what is not water plus .75 times water.
since the new solution is 9.6 grams and the old solution is 6 grams, you added 3.6 grams of water.
another way to look at it which might be more conventional would be to look at the original equation and solve as follows.
let x be what is not water.
let y be what is water.
let z be the total solution.
you start out with .4z + .6z = 6 grams
you get x = .4z = 2.4 grams
you get y = .6z = 3.6 grams
let k be the amount of water you are going to add to the solution.
your new solution will be:
(.25 * (z+k)) + (.75 * (z+k)) = z + k
you know that z is 6 so your equation becomes
(.25*(6+k)) + (.75*(6+k) = 6+k
you know that .25 * (6+k) will remain the same which will be 2.4 grams. this is what is not water.
your equation becomes
2.4 + (.75*(6+k)) = 6+k
you simplify to get
2.4 + (.75*6) + (.75*k) = 6+k
you simplify further to get
2.4 + 4.5 + .75*k = 6 + k
you simplify further to get
6.9 + .75*k = 6 + k
you subtract 6 from both sides of the equation and you subtract .75*k from both sides of the equation to get
.9 = .25*k
you divide both sides of the equation by .25 to get
.9/.25 = k
you simplify to get
3.6 = k
this is the same answer we got earlier.
it looks correct.
the total solution is 6 + 3.6 = 9.6 grams.
.25 * 9.6 = 2.4 grams of what is not water.
.75 * 9.6 = 7.2 grams of what is water.
