SOLUTION: A chemist needs 180 milliliters of a 61% solution but has only 54% and 72% solutions available. Find how many milliliters of each that should be mixed to get the desired solution?

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Question 736477: A chemist needs 180 milliliters of a 61% solution but has only 54% and 72% 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 54% solution needed
Let +b+ = ml of 72% solution needed
given:
(1) +a+%2B+b+=+180+
(2) +%28+.54a+%2B+.72b+%29+%2F+180+=+.61+
------------------------------
(2) +.54a+%2B+.72b+=+.61%2A180+
(2) +.54a+%2B+.72b+=+109.8+
(2) +54a+%2B+72b+=+10980+
Multiply both sides of (1) by +54+
and subtract (1) from (2)
(2) +54a+%2B+72b+=+10980+
(1) +-54a+-+54b+=+-9720+
+18b+=+1260+
+b+=+70+
and, since
(1) +a+%2B+b+=+180+
(1) +a+=+110+
110 ml of 54% solution is needed
70 ml of 72% solution is needed
check:
(2) +%28+.54%2A110+%2B+.72%2A70+%29+%2F+180+=+.61+
(2) ++59.4+%2B+50.4+=+109.8+
(2) +109.8+-+109.8+
OK