SOLUTION: How many ounces of a 31% alcohol solution and a 41% alcohol solution must be combined to form 40 ounces of a 40% alcohol solution?

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Question 871590: How many ounces of a 31% alcohol solution and a 41% alcohol solution must be combined to form 40 ounces of a 40% alcohol solution?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = ounces of 31% solution needed
Let +b+ = ounces of 41% solution needed
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(1) +a+%2B+b=+40+
(2) +%28+.31a+%2B+.41b+%29+%2F+40++=+.4+
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(2) +.31a+%2B+.41b+=+16+
(2) +31a+%2B+41b+=+1600+
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Multiply both sides of (1) by +31+
and subtract (1) from (2)
(2) +31a+%2B+41b+=+1600+
(1) +-31a+-+31b+=+-1240+
+10b+=+360+
+b+=+36+
and, since
(1) +a+%2B+b=+40+
(1) +a+=+4+
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4 ounces of 31% solution are needed
36 ounces of 41% solution are needed
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check:
(2) +%28+.31a+%2B+.41b+%29+%2F+40++=+.4+
(2) +%28+.31%2A4+%2B+.41%2A36+%29+%2F+40++=+.4+
(2) +%28+1.24+%2B+14.76+%29+%2F+40+=+.4+
(2) +16%2F40+=+.4+
(2) +16+=+16+
OK