SOLUTION: A chemist needs 12 liters of a 36% acid solution. How many liters of 18% acid should be combined with a 45% acid solution to obtain the proper mixture? My teacher didn't teach u

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Question 617776: A chemist needs 12 liters of a 36% acid solution. How many liters of 18% acid should be combined with a 45% acid solution to obtain the proper mixture?
My teacher didn't teach us this at all. Please, provide an explanation.
Found 2 solutions by josmiceli, scott8148:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a = liters of 18% solution needed
Let +b+ = liters of 45% solution needed
+.18a+ = liters of acid in 18% solution
+.45b+ = liters of acid in 45% solution
------------------
given:
(1) +a+%2B+b+=+12+
(2) +%28+.18a+%2B+.45b+%29+%2F+12+=+.36+
--------------------------
(2) +.18a+%2B+.45b+=+.36%2A12+
(2) +.18a+%2B+.45b+=+4.32+
(2) +18a+%2B+45b+=+432+
Multiply both sides of (1) by +18+
and subtract (1) from (2)
(2) +18a+%2B+45b+=+432+
(1) +-18a+-+18b+=+-216+
+27b+=+216+
+b+=+8+
and, since
(1) +a+%2B+b+=+12+
(1) +a+=+4+
4 liters of 18% solution are needed
12 liters of 45% solution are needed

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
the equation(s) are set up based on the "active" ingredient -- in this case, the acid

the final product is 12L of 36% acid
___ to get that, you mix some amount of 18% acid; with -- 12L minus that amount -- of 45% acid

(x)(18%) + (12 - x)(45%) = (12)(36%) ___ multiplying by 100 to clear the percents is usually a good idea

18x + (12 * 45) - 45x = (12 * 36)

(12 * 45) - (12 * 36) = 45x - 18x

12 * 9 = 27x ___ 4 = x