SOLUTION: a nurse needs rubbing alcohol, which is a 70% alcohol solution. However, there is only a 40% alcohol solution and a 90% alcohol solution in stock. how much of each solution should

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Question 1093599: a nurse needs rubbing alcohol, which is a 70% alcohol solution. However, there is only a 40% alcohol solution and a 90% alcohol solution in stock. how much of each solution should be mixed in order to obtain 8 ounces of the desired solution?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = ounces of 40% solution needed
Let +b+ = ounces of 90% solution needed
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(1) +a+%2B+b+=+8+
(2) +%28+.4a+%2B+.9b+%29+%2F+8+=+.7+
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(2) +.4a+%2B+.9b+=+5.6+
(2) +4a+%2B+9b+=+56+
Multiply both sides of (1) by +4+
and subtract (1) from (2)
-----------------------------------
(2) +4a+%2B+9b+=+56+
(1) +-4a+-+4b+=+-32+
--------------------------
+5b+=+24+
+b+=+4.8+
and
(1) +a%2B+b+=+8+
(1) +a+=+8+-+4.8+
(1) +a+=+3.2+
-----------------------
3.2 ounces of 40% solutions are needed
4.8 ounces of 90% solution are needed
-------------------------------------
check:
(2) +%28+.4a+%2B+.9b+%29+%2F+8+=+.7+
(2) +%28+.4%2A3.2+%2B+.9%2A4.8+%29+%2F+8+=+.7+
(2) +1.28+%2B+4.32+=+5.6+
(2) +5.6+=+5.6+
OK