SOLUTION: How many liters (L) of a 30% ACID SOLUTION MUST BE ADDED TO 8 L of an 55% acid solution to obtain a 40% solution?

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: How many liters (L) of a 30% ACID SOLUTION MUST BE ADDED TO 8 L of an 55% acid solution to obtain a 40% solution? This question is from textbook

Answer by josmiceli(19441) About Me  (Show Source):
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Let a = amount of 30% acid solution needed
Let b = amount of 55% acid solution
Given is b+=+8liters
(acid in 30% and 55% solutions)/(total solution) = 40%
%28.3a+%2B+.55b%29+%2F+%28a+%2B+b%29+=+.4
%28.3a+%2B+.55%2A8%29+%2F+%28a+%2B+8%29+=+.4
.3a+%2B+4.4+=+.4%28a+%2B+8%29
.3a+%2B+4.4+=+.4a+%2B+3.2
.1a+=+1.2
a+=+12liters
12 liters of the 30% solution must be added
check:
%28.3%2A12+%2B+.55%2A8%29+%2F+20+=+.4
3.6+%2B+4.4+=+20%2A.4
8+=+8
OK