SOLUTION: taylor is a chemist. she needs to prepare 32 ounces of a 12% hydrochloric acid solution. find the amount of a 16% solution and the amount of 8% solution she should mix to get this

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: taylor is a chemist. she needs to prepare 32 ounces of a 12% hydrochloric acid solution. find the amount of a 16% solution and the amount of 8% solution she should mix to get this      Log On


   



Question 497608: taylor is a chemist. she needs to prepare 32 ounces of a 12% hydrochloric acid solution. find the amount of a 16% solution and the amount of 8% solution she should mix to get this
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = ounces of 16% hydrochloric acid solution needed
Let b = ounces of 8% hydrochloric acid solution needed
given:
(1) +a+%2B+b+=+32+
(2) +.16a+%2B+.08b+=+.12%2A32+
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(2) +.16a+%2B+.08b+=+3.84+
Multiply both sides of (2) by 100
(2) +16a+%2B+8b+=+384+
Multiply both sides of (1) by 8
and subtract (1) from (2)
(2) +16a+%2B+8b+=+384+
(1) -8+a+-+8b+=+256+
+8a+=+128+
+a+=+16+
and, since
(1) +a+%2B+b+=+32+
(1) +b+=+16+
16 ounces of 16% hydrochloric acid solution are needed
16 ounces of 8% hydrochloric acid solution are needed
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check answer:
(2) +.16%2A16+%2B+.08%2A16+=+3.84+
(2) +2.56+%2B+1.28+=+3.84+
(2) +3.84+=+3.84+
OK