SOLUTION: Rx: zink oxide 20% ointment 90g. how many grams of zink oxide 40% ointment and zink oxide 10% ointment should you mix to prepare the prescription.

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Question 629214: Rx: zink oxide 20% ointment 90g. how many grams of zink oxide 40% ointment and zink oxide 10% ointment should you mix to prepare the prescription.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = grams of 40% ointment needed
Let +b+ = grams of 10% ointment needed
given:
(1) +a+%2B+b+=+90+
(2) +%28+.4a+%2B+.1b+%29+%2F+90+=+.2+
-------------------------
(2) +.4a+%2B+.1b+=+.2%2A90+
(2) +.4a+%2B+.1b+=+18+
(2) +4a+%2B+b+=+180+
Subtract (1) from (2)
(2) +4a+%2B+b+=+180+
(1) +-a+-+b+=+-90+
+3a+=+90+
+a+=+30+
and, since
(1) +a+%2B+b+=+90+
(1) +30+%2B+b+=+90+
(1) +b+=+60+
30 grams of 40% ointment are needed
60 grams of 10% ointment are needed
check:
(2) +%28+.4%2A30+%2B+.1%2A60+%29+%2F+90+=+.2+
(2) +%28+12+%2B+6+%29+%2F+90+=+.2+
(2) +18%2F90+=+.2+
(2) +18+=+18+
OK