SOLUTION: A pharmacist mixed some 10%-saline solution with some 15%-saline solution to obtain 100 mL of a 12%-saline solution. How much of the 10%-saline solution did the pharmacist use in t

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Question 606141: A pharmacist mixed some 10%-saline solution with some 15%-saline solution to obtain 100 mL of a 12%-saline solution. How much of the 10%-saline solution did the pharmacist use in the mixture?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = ml of 10% solution needed
Let +b+ = ml of 15% solution needed
+.1a+ = ml of salt in 10% solution
+.15b+ = ml of salt in 15% solution
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(1) +%28+.1a+%2B+.15b+%29+%2F+100+=+.12+
(2) +a+%2B+b+=+100+
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(1) +.1a+%2B+.15b+=+12+
(1) +10a+%2B+15b+=+1200+
Multiply both sides of (2) by +10+
and subtract (2) from (1)
(1) +10a+%2B+15b+=+1200+
(2) +-10a+-+10b+=+-1000+
+5b+=+200+
+b+=+40+
and, since
(2) +a+%2B+b+=+100+
(2) +a+%2B+40+=+100+
(2) +a+=+100+-+40+
(2) +a+=+60+
60 ml of 10% solution is needed
check answer
(1) +%28+.1a+%2B+.15b+%29+%2F+100+=+.12+
(1) +%28+.1%2A60+%2B+.15%2A40+%29+%2F+100+=+.12+
(1) ++6+%2B+6+=+.12%2A100+
(1) +12+=+12+
OK