SOLUTION: How many mL of a 20% acid should Paul mix with a 60% acid solution to make 100 mL of 50% acid solution?

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Question 691502: How many mL of a 20% acid should Paul mix with a 60% acid solution to make 100 mL of 50% acid solution?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = ml of 20% solution needed
Let +b+ = ml of 60% solution needed
given:
(1) +a+%2B+b+=+100+
(2) +%28+.2a+%2B+.6b+%29+%2F+100+=+.5+
---------------------------
(2) +.2a+%2B+.6b+=+50+
(2) +2a+%2B+6b+=+500+
Multiply both sides of (1) by +2+
and subtract (1) from (2)
(2) +2a+%2B+6b+=+500+
(1) +-2a++-+2b+=+-200+
+4b+=+300+
+b+=+75+
and, since
(1) +a+%2B+b+=+100+
(1) +a+%2B+75+=+100+
(1) +a+=+25+
25 ml of 20% solution is needed
75 ml of 60% solution is needed
check:
(2) +%28+.2a+%2B+.6b+%29+%2F+100+=+.5+
(2) +%28+.2%2A25+%2B+.6%2A75+%29+%2F+100+=+.5+
You can finish the check