How do I solve this word problem?

Question

A health clinic uses a solution of bleach to sterilize petri dishes in which cultures are grown. The sterilization tank contains 120 gal of a solution of 4% ordinary household bleach mixed with pure distilled water. New research indicates that the concentration of bleach should be 5% for complete sterilization. How much of the solution should be drained and replaced with bleach to increase the bleach content to the recommended level?

Answer 1

X is the amount that is poured out and replaced with pure bleach.

The amount of bleach is then:

 

 Amount remaining + amount bleach =  amount new solution that is 5% pure bleach

     (120-X)*0.04    +    1*  X            =    120*0.05

       120*0.04  - X * 0.04  + 1* X = 120 * 0.05 <--- distributive property left side

              4.8        - 0.04X + 1.00*X  = 6

                  0.96X = 6 - 4.8  <--- combines like terms on left side; subtracts 4.8 from both sides

                   0.96X = 1.2

                    96X = 120   <--- multiplies both sides by 100 to clear the decimals

                     X = 120/96 = 60/48 = 30/24 = 15/12 = 5/4 = 1.25

CHECK:
(120 - 1.25)*0.04 + 1.25 =

118.75 * 0.04 + 1.25 = 6

 

Pour out 1.25 gallons of the old solution and replace it with 1.25 gallons of pure bleach.

Answer 2

(0.04)120    the amount of bleach present

0.04x          the amount of bleach removed

x                 the amount of bleach added

(0.05)(120)  the amount of bleach resulting

 

(0.04)120 - 0.04x + x = (0.05(120)

 

Can you solve for x and answer?