SOLUTION: How much of 40% alcohol and how much of 80% solution should be mixed to give 40 gallons of 50% solution?

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Question 770735: How much of 40% alcohol and how much of 80% solution should be mixed to give 40 gallons of 50% solution?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = gallons of 40% solution needed
Let +b+ = gallons of 80% solution needed
+.4a+ = gallons of alcohol in 40% solution
+.8b+ = gallons of alcohol in 80% solution
----------------------
(1) +a+%2B+b+=+40+
(2) +%28+.4a+%2B+.8b+%29+%2F+40+=+.5+
--------------------------
(2) +.4a+%2B+.8b+=+.5%2A40+
(2) +.4a+%2B+.8b+=+20+
(2) +4a+%2B+8b+=+200+
(2) +a+%2B+2b+=+50+
Subtract (1) from (2)
(2) +a+%2B+2b+=+50+
(1) +-a+-+b+=+-40+
+b+=+10+
and, since
(1) +a+%2B+b+=+40+
(1) +a+=+30+
30 gallons of 40% solution are needed
10 gallons of 80% solution are needed
check:
(2) +%28+.4%2A30+%2B+.8%2A10+%29+%2F+40+=+.5+
(2) +%28+12+%2B+8+%29+%2F+40+=+.5+
(2) +20+=+.5%2A40+
(2) +20+=+20+
OK