SOLUTION: How much water should be added to 20mL of ​18% alcohol solution to reduce the concentration to 10​%?

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Question 1175630: How much water should be added to 20mL of ​18% alcohol solution to reduce the concentration to 10​%?
Found 2 solutions by ikleyn, VFBundy:
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.

    %280.18%2A20%29%2F%2820%2Bw%29 = 0.1


    3.6                    = 0.1*(20+w)

    3.6                    = 2 + 0.1w

    3.6 - 2                = 0.1w

    1.6                    = 0.1w

      w                    = 1.6%2F0.1 = 16.


ANSWER.  16 mL of water should be added.


CHECK.   %280.18%2A20%29%2F%2820%2B16%29 = 3.6%2F36 = 0.1 = 10% concentration.   ! Correct !


It can be solved mentally, too. 


    20 mL of the 18% solution contain  0.18*20 = 3.6 mL pure alcohol.


    To have 10% solution, the total volume must be  36 mL;


    hence,  16 = 36-20  milliliters of water must be added.


The second solutions provides THE SAME answer.



Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
%280.18%2A%2820%29%29%2F%2820+%2B+x%29 = 0.10

3.6%2F%2820+%2B+x%29 = 0.10

0.10(20 + x) = 3.6

2 + 0.10x = 3.6

0.10x = 1.6

x = 16