SOLUTION: What quantity of 80 per cent acid solution must be mixed with a 20 per cent solution to produce 120 mL of a 50 per cent solution? -Please explain the steps also, not just the an

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Question 800405: What quantity of 80 per cent acid solution must be mixed with a 20 per cent solution to produce 120 mL of a 50 per cent solution?
-Please explain the steps also, not just the answer. So I can understand it better :)

Found 2 solutions by josmiceli, stanbon:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = ml of 80% solution needed
+.8a+ = ml of acid in 80% solution
Let +b+ = ml of 20% solution needed
+.2b+ = ml of acid in 20% solution
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(1) +a+%2B+b+=+120+
(2) +%28+.8a+%2B+.2b+%29+%2F+120+=+.5+
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(2) +.8a+%2B+.2b+=+.5%2A120+
(2) +.8a+%2B+.2b+=+60+
(2) +8a+%2B+2b+=+600+
(2) +4a+%2B+b+=+300+
Subtract (1) from (2)
(2) +4a+%2B+b+=+300+
(1) +-a+-+b+=+-120+
+3a+=+180+
+a+=+60+
and, since
(1) +a+%2B+b+=+120+
(1) +b+=+60+
60 ml of 80% acid solution are needed
check:
(2) +%28+.8%2A60+%2B+.2%2A60+%29+%2F+120+=+.5+
(2) +%28+48+%2B+12+%29+%2F+120+=+.5+
(2) +60+=+.5%2A120+
(2) +60+=+60+
OK

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
What quantity of 80 per cent acid solution must be mixed with a 20 per cent solution to produce 120 mL of a 50 per cent solution?
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Equation:
acid + acid = acid
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0.80x + 0.20(120-x) = 0.50*120
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80x + 20*120 - 20x = 50*120
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60x = 30*120
x = 60 mL (amt. of 80% solution needed)
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120-60 = 60 mL (amt. of 20% solution needed)
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Cheers,
Stan H.
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