Applications involving mixtures

Question

How much pure bleach should tim combine with a solution that is 4% bleach to make 12 ounces of a 12% bleach solution(hint: pure bleach is 100% bleach)

Answer 1

Hi Amber,

 

So we need to blend pure bleach with 4% bleach to make 12 ounces of 12% bleach.

 

In 12 ounces of 12% bleach, we have 12 *.12= 1.44 ounces of pure bleach.

 

we need a formula to find the answer.

 

The total ounces are 12,  The ounces of 4% we will call X and so the amount of pure bleach is 12 - X

 

The percentages of bleach from each solution is .04X from the 4% solution and (12-X) from the pure bleach

 

.04X + (12 - X) = 1.44 ounces of pure bleach

 

12 - 0.96X = 1.44

 

0.96X = 10.56

 

X = 11 ounces of 4% solution

 

12 - X = 1 ounce of pure bleach

 

 

We can check the answer by simple math

 

(11*4% + 1*100%) / 12 = (.44 + 1) / 12 = 1.44 / 12 = .12 = 12%  Q.E.D.

 

FYI Q.E.D. is the initials of "quod erat demonstrandum" a latin phrase meaning "which had to be proven".

 

I hope this helps.

 

Sincerely,

Ralph K.

Answer 2

Hi Amber,

 

OK so mixture problems like this should be set up as follows

 

Percent 1 * amount of solution1 + Percent 2 * amount of solutionn 2 = Final Percent * amount of combined solution

 

Now lets put the values in from above and solve for the item we need to find

 

let x = amount of solution 1

12-x = amounti of solution 2   (since the combined total of the two is 12

 

4% * (x)  + 100% (12-x) = 12% * 12

 

.04x + 12 -x = .12 * 12

 

-.96x = 1.44 -12

 

-.96x = -10.56

 

x = 11   ( amount of the 4% solution

 

12-x = 1   (amount of the 100% solution

 

Hope this helps