SOLUTION: you need to use 3 solutions of drug H containing respectively 50%, 20%, and 5% to make 600ml of 10% drug H. How much of the 50% will you use? Who try to solve it for me.

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Question 601799: you need to use 3 solutions of drug H containing respectively 50%, 20%, and 5% to make 600ml of 10% drug H. How much of the 50% will you use?
Who try to solve it for me.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = ml of 50% solution needed
Let +b+ = ml of 20% solution needed
Let +c+ = ml of 5% solution needed
given:
(1) +a+%2B+b+%2B+c+=+600+ ml
(2) +%28+.5a+%2B+.2b+%2B+.05c+%29+%2F+600+=+.1+
This is only 2 equations and 3 unknowns,
but I can guess at a solution
--------------------------------
(2) +.5a+%2B+.2b+%2B+.05c+=+60+
(2) +50a+%2B+20b+%2B+5c+=+6000+
Multiply both sides of (1) by +5+ and
subtract (1) from (2)
(2) +50a+%2B+20b+%2B+5c+=+6000+
(1) +-5a+-+5b+-+5c+=+3000+
+45a+%2B+15b+=+3000+
+3a+%2B+b+=+200+
I'll guess that +a+=+50+ and +b+=+50+
then
(2) +50a+%2B+20b+%2B+5c+=+6000+
(2) +50%2A50+%2B+20%2A50+%2B+5c+=+6000+
(2) +2500+%2B+1000+%2B+5c+=+6000+
(2) +3500+%2B+5c+=+6000+
(2) +5c+=+2500+
(2) +c+=+500+
That works, so I can use
50 ml of 50% solution needed
50 ml of 20% solution needed
500 ml of 5% solution needed
There can be other solutions, but this works