SOLUTION: how many quarts of 30% soap solution and 60% soap solution should be mixed to obtain 60 quarts of 50 % soap solution?

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Question 292646: how many quarts of 30% soap solution and 60% soap solution should be mixed to obtain 60 quarts of 50 % soap solution?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
In words:
(total quarts of soap)/(total quarts of solution) = 50%
Let a = quarts of 30% solution
Let b = quarts of 60% solution
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given:
a+%2B+b+=+60
b+=+60+-+a
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%28.3a+%2B+.6b%29%2F60+=+.5
.3a+%2B+.6b+=+30
3a+%2B+6b+=+300
a+%2B+2b+=+100
By substitution:
a+%2B+2%2A%2860+-+a%29+=+100
a+%2B+120+-+2a+=+100
-a+=+-20
a+=+20
and, since
a+%2B+b+=+60
b+=+60+-+20
b+=+40
20 quarts of 30% solution and 40 quarts of 60% solution are needed
check:
%28.3a+%2B+.6b%29%2F60+=+.5
%28.3%2A20+%2B+.6%2A40%29%2F60+=+.5
%286+%2B+24%29%2F60+=+.5
30%2F60+=+.5
.5+=+.5
OK