SOLUTION: a lab technician needs to mix a 45% phosphorus solution with an 18% phosphorus solution to obtain 12 milliliters of a 36% phosphorus solution. how many milliliters of the 18% phosp

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Question 954363: a lab technician needs to mix a 45% phosphorus solution with an 18% phosphorus solution to obtain 12 milliliters of a 36% phosphorus solution. how many milliliters of the 18% phosphorus solution will the lab technician need?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = ml of 45% solution needed
+.45a+ = ml of phosphorus in 45% solution
Let +b+ = ml of 18% solution needed
+.18b+ = ml of phosphorus in 18% solution
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(1) +a+%2B+b+=+12+
(2) +%28+.45a+%2B+.18b+%29+%2F+12+=+.36+
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(2) +.45a+%2B+.18b+=+.36%2A12+
(2) +.45a+%2B+.18b+=+4.32+
(2) +45a+%2B+18b+=+432+
Divide both sides by +9+
(2) +5a+%2B+2b+=+48+
Multiply both sides of (1) by 2 and
subtract (1) from (2)
(2) +5a+%2B+2b+=+48+
(1) +-2a+-+2b+=+-24+
-----------------------
+3a+=+24+
+a+=+8+
and
(1) +8+%2B+b+=+12+
(1) +b+=+4+
------------------
4 ml of the 18% solution are needed
check:
(2) +%28+.45a+%2B+.18b+%29+%2F+12+=+.36+
(2) +%28+.45%2A8+%2B+.18%2A4+%29+%2F+12+=+.36+
(2) +%28+3.6+%2B+.72+%29+%2F+12+=+.36+
(2) +4.32+=+.36%2A12+
(2) +4.32+=+4.32+
OK