SOLUTION: How many gallons of a 3% salt solution must be mixed with 10 gallons of a 8% solution to obtain a 4% solution

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Question 404584: How many gallons of a 3% salt solution must be mixed with 10 gallons of a 8% solution to obtain a 4% solution
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = gallons of 3% solution needed
In words:
(gallons of salt in final solution)/(total final solution) = 4%
given:
.03a = gallons of salt in 3% solution
.08%2A10+=+.8 = gallons of salt in 8% solution
-------------------------------------
%28.03a+%2B+.8%29%2F%28a+%2B+10%29+=+.04
.03a+%2B+.8+=+.04%2A%28a+%2B+10%29
.03a+%2B+.8+=+.04a+%2B+.4
.01a+=+.4
a+=+40 gallons
40 gallons of a 3% solution must be added
check answer:
%28.03a+%2B+.8%29%2F%28a+%2B+10%29+=+.04
%28.03%2A40+%2B+.8%29%2F%2840+%2B+10%29+=+.04
%281.2+%2B+.8%29%2F50+=+.04
2%2F50+=+.04
2+=+50%2A.04
2+=+2
OK