SOLUTION: I have a 17% salicylic acid solution that I have to mix with alcohol to make a 2% solution to use as a face toner. The alcohol bottle I have is 473 mL total. What amount of each do

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: I have a 17% salicylic acid solution that I have to mix with alcohol to make a 2% solution to use as a face toner. The alcohol bottle I have is 473 mL total. What amount of each do      Log On

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Question 740906: I have a 17% salicylic acid solution that I have to mix with alcohol to make a 2% solution to use as a face toner. The alcohol bottle I have is 473 mL total. What amount of each do I have to use to get the 2%?
Thanks!
Found 2 solutions by josmiceli, josgarithmetic:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = ml of 17% solution needed
Let +b+ = ml of alcohol needed
+.17a+ = ml of salicylic acid in 17% solution
-----------------
(1) +a+%2B+b+=+473+
(2) +.17a+%2F+473+=+.02+
----------------------
(2) +.17a+=+.02%2A473+
(2) +.17a+=+9.46+
(2) +a+=+55.647+
and, since
(1) +a+%2B+b+=+473+
(1) +b+=+473+-+55.647+
(1) +b+=+417.353+
55.647 ml of 17% solution is needed
417.353 ml of alcohol is needed
check:
(2) +.17a+%2F+473+=+.02+
(2) +.17%2A55.647+%2F+473+=+.02+
(2) +9.46+%2F+473+=+.02+
(2) +9.46+=+.02%2A473+
(2) +9.46+=+9.46+
OK

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
(Amount of salicylic acid)/(amount of solution)=concentration of salicylic acid

Let v = volume of salicylic acid to use.
Let r = volume of the alcohol to use.
volumes are in milliliters.

17%2Av%2F%28v%2Br%29=2 and v%2Br=473
Solve for v and r.