SOLUTION: According to new hospital standards a certain disinfectant solution needs to be 20% alcohol instead of 10% alcohol. There is a 40% alcohol disinfectant available to adjust the mixt

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: According to new hospital standards a certain disinfectant solution needs to be 20% alcohol instead of 10% alcohol. There is a 40% alcohol disinfectant available to adjust the mixt      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 810099: According to new hospital standards a certain disinfectant solution needs to be 20% alcohol instead of 10% alcohol. There is a 40% alcohol disinfectant available to adjust the mixture. Determine the amount of 10% solution and the amount of 40% solution to produce 30L of a 20% solution.
I am not sure on where to start and my teacher has not gone over any similar problems so I am really stuck. Please help me!?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = liters of 10% solution needed
Let +b+ = liters of 40% solution needed
-----------------
(1) +a+%2B+b+=+30+ liters
(2) +%28+.1a+%2B+.4b+%29+%2F+30+=+.2+
--------------------------
(2) +.1a+%2B+.4b+=+6+
(2) +a+%2B+4b+=+60+
Subtract (1) from (2)
(2) +a+%2B+4b+=+60+
(1) +-a+-+b+=+-30+
+3b+=+30+
+b+=+10+
and, since
(1) +a+%2B+b+=+30+
(1) +a+=+20+
20 liters of 10% solution is needed
10 liters of 40% solution is needed
---------------------------
check answer:
(2) +%28+.1a+%2B+.4b+%29+%2F+30+=+.2+
(2) +%28+.1%2A20+%2B+.4%2A10+%29+%2F+30+=+.2+
(2) +%28+2+%2B+4+%29+%2F+30+=+.2+
(2) +6%2F30+=+.2+
(2) +6+=+.2%2A30+
(2) +6+=+6+
OK