SOLUTION: Assef wants to create 50 oz of isopropyl solution of strength 78%.he has on hand some isopropyl solution of strengths 50% and 90%. how much of each solution should be used

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Question 579474: Assef wants to create 50 oz of isopropyl solution of strength 78%.he has on hand some isopropyl solution of strengths 50% and 90%. how much of each solution should be used
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = ounces of 50% solution needed
Let +b+ = ounces of 90% solution needed
given:
(1) +a+%2B+b+=+50+ ounces
(2) +%28+.5a+%2B+.9b+%29+%2F+50+=+.78+
------------------------
(2) +.5a+%2B+.9b+=+.78%2A50+
(2) +.5a+%2B+.9b+=+39+
(2) +5a+%2B+9b+=+390+
Multiply both sides of (1) by +5+
and subtract (1) from (2)
(2) +5a+%2B+9b+=+390+
(1) +-5a+-+5b+=+-250+
+4b+=+140+
+b+=+35+
and, since
(1) +a+%2B+b+=+50+
(1) +a+%2B+35+=+50+
(1) +a+=+50+-+35+
(1) +a+=+15+
15 ounces of 50% solution is needed
35 ounces of 90% solution is needed
check answer:
(2) +%28+.5%2A15+%2B+.9%2A35+%29+%2F+50+=+.78+
(2) +%28+7.5+%2B+31.5+%29+%2F+50+=+.78+
(2) +39%2F50+=+.78+
(2) +39+=+.78%2A50+
(2) +39+=+39+
OK