SOLUTION: a chemist needs 120 milliliters of a 30% solution but only has only 14% and 38% solutions available. Find how many milliliters of each that should be mixed to get the desired solut

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Question 944272: a chemist needs 120 milliliters of a 30% solution but only has only 14% and 38% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = ml of 14% solution needed
Let +b+ = ml of 38% solution needed
-------------------------------------
(1) +a+%2B+b+=+120+
(2) +%28+.14a+%2B+.38b+%29+%2F+120+=+.3+
-------------------------------
(2) +.14a+%2B+.38b+=+.3%2A120+
(2) +.14a+%2B+.38b+=+36+
(2) +14a+%2B+38b+=+3600+
Multiply both sides of (1) by +14+
and subtract (1) from (2)
(2) +14a+%2B+38b+=+3600+
(1) +-14a+-+14b+=+-1680+
---------------------------
+24b+=+1920+
+b+=+80+
and, since
(1) +a+%2B+b+=+120+
(1) +a+=+40+
40 ml of 14% solution is needed
80 ml of 38% solution is needed
check:
(2) +%28+.14%2A40+%2B+.38%2A80+%29+%2F+120+=+.3+
(2) +%28+5.6+%2B+30.4+%29+%2F+120+=+.3+
(2) +36+=+.3%2A120+
(2) +36+=+36+
OK