SOLUTION: How much 9% HC1 must be mixed with 4% HC1 to produce 50mL of 6% HC1?

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Question 958179: How much 9% HC1 must be mixed with 4% HC1 to produce 50mL of 6% HC1?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = ml of 9% HCL needed
Let +b+ = ml of 4% HCL needed
--------------------
(1) +a+%2B+b+=+50+ ml
(2) +%28+.09a+%2B+.04b+%29+%2F+50+=+.06+
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(2) +.09a+%2B+.04b+=+.06%2A50+
(2) +.09a+%2B+.04b+=+3+
(2) +9a+%2B+4b+=+300+
---------------------
Multiply both sides of (1) by +4+
and subtract (1) from (2)
(2) +9a+%2B+4b+=+300+
(1) +-4a+-+-4b+=+-200+
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+5a+=+100+
+a+=+20+
and
(1) +20+%2B+b+=+50+
(2) +b+=+30+
20 ml of 9% HCL are needed
30 ml of 4% HCL are needed
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check:
(2) +%28+.09%2A20+%2B+.04%2A30+%29+%2F+50+=+.06+
(2) +%28+1.8+%2B+1.2+%29+%2F+50+=+.06+
(2) +3+=+.06%2A50+
(2) +3+=+3+
OK