SOLUTION: How many liters of each of 20% acid solution and 45% acid solution must be used to produce 50 liters of a 40% acid solution?

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Question 693621: How many liters of each of 20% acid solution and 45% acid solution must be used to produce 50 liters of a 40% acid solution?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = liters of 20% solution needed
Let +b+ = liters of 45% solution needed
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given:
(1) +a+%2B+b+=+50+
(2) +%28+.2a+%2B+.45b+%29+%2F+50+=+.4+
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(2) +.2a+%2B+.45b+=+.4%2A50+
(2) +20a+%2B+45b+=+2000+
Multiply both sides of (1) by +20+
and subtract (1) from (2)
(2) +20a+%2B+45b+=+2000+
(1) +-20a+-+20b+=+-1000+
+25b+=+1000+
+b+=+40+
and, since
(1) +a+%2B+b+=+50+
(1) +a+%2B+40+=+50+
(1) +a+=+10+
10 liters of 20% solution are needed
40 liters of 45% solution are needed
check:
(2) +%28+.2a+%2B+.45b+%29+%2F+50+=+.4+
(2) +%28+.2%2A10+%2B+.45%2A40+%29+%2F+50+=+.4+
(2) +%28+2+%2B+18+%29+%2F+50+=+.4+
(2) +20%2F50+=+.4%0D%0A%282%29+%7B%7B%7B+20+=+.4%2A50+
(2) +20+=+20+
OK