SOLUTION: What quantity of 75 per cent acid solution must be mixed with a 25 per cent solution to produce 1080 mL of a 50 per cent solution?

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Question 706349: What quantity of 75 per cent acid solution must be mixed with a 25 per cent solution to produce 1080 mL of a 50 per cent solution?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = mL of 75% solution needed
Let +b+ = mL of 25% solution needed
given:
(1) +a+%2B+b+=+1080+
(2) +%28+.75a+%2B+.25b+%29+%2F+1080+=+.5+
------------------------------
(2) +.75a+%2B+.25b+=+.5%2A1080+
(2) +.75a+%2B+.25b+=+540+
(2) +75a+%2B+25b+=+54000+
Multiply both sides of (1) by +25+
and subtract (1) from (2)
(2) +75a+%2B+25b+=+54000+
(1) +-25a+-+25b+=+-27000+
+50a+=+27000+
+a+=+540+
and
(1) +540+%2B+b+=+1080+
(1) +b+=+540+
540 mL of 75% acid solution must be used
check:
(2) +%28+.75%2A540+%2B+.25%2A540+%29+%2F+1080+=+.5+
(2) +%28+405+%2B+135+%29+%2F+1080+=+.5+
(2) +540+=+.5%2A1080+
(2) +540+=+540+
OK