Question 838678: I have a 300ml solution of 14% bleach but need to make it into 10% how much water do I add? Found 4 solutions by ewatrrr, richwmiller, amalm06, ikleyn:Answer by ewatrrr(24785) (Show Source):
Hi,
I have a 300ml solution of 14% bleach(84% water) but need to make it into 10% (90% water)
how much water do I add?
Let x represent the ml of water added
water = water x = 180ml of water must be added
You can put this solution on YOUR website! from view of bleach
.14*(300)=.1(300+x),
42=30+.1x
12=.1x
120=x
or from view of water
.86*(300)+y=.9(300+y)
258+y=270+.9y
.1y=12
y=120
You can put this solution on YOUR website! Let B denote bleach and W denote water
Using the method of alligation,
0.14-0.10=0.04
0.10-0=0.10
B/W=0.10/0.04 --> 0.10/0.04=300/W --> W=120 mL (Answer)
Let W be the volume of water (in mL) to add to your original solution.
When you add, your final solution will have the volume of (300+W) mL.
This volume will contain the same 0.14*300 mL of bleach as the original solution.
So, the concentration of the final solution will be this ratio of the "pure bleach" to the total liquid volume.
According to the condition, this ratio must be equal to 10%, or 0.1.
It gives you an equation
= 0.1.
It is your major/basic equation for the given problem.
As soon as you got this equation, the setup part is done and completed.
This equation is often called a "concentration" equation, since its both sides describe the concentration of the final solution.
To solve the equation, multiply both sides by (300+W). You will get
0.14*300 = 0.1*(300 + W),
0.14*300 = 0.1*300 + 0.1*W,
0.14*300 - 0.1*300 = 0.1*W ====> 0.04*300 = 0.1*W ====> W = = 0.4*300 = 120.
Answer. You need to add 120 mL of water.
Check. = 0.1 = 10%. ! Correct !
