SOLUTION: 1 (solving systems of equations)-how many gallons of a 5% solution should be mixed with 30 gallons of a 10% solution to obtain a mixture that is 8%?

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Question 162060: 1 (solving systems of equations)-how many gallons of a 5% solution should be mixed with 30 gallons of a 10% solution to obtain a mixture that is 8%?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
In words:
(gallons of stuff in 5%) + (gallons of stuff in 10%) / total mixture = 8%
Let the gallons of the 5% solution needed = x
%28.05x+%2B+.1%2A30%29+%2F+%28x+%2B+30%29+=+.08
Multiply both sides by x+%2B+30
.05x+%2B+3+=+.08%2A%28x+%2B+30%29
.05x+%2B+3+=+.08x+%2B+2.4
.03x+=+.6
x+=+20gal
20 gallons of the 5% solution are needed
check answer:
%28.05x+%2B+.1%2A30%29+%2F+%28x+%2B+30%29+=+.08
%28.05%2A20+%2B+.1%2A30%29+%2F+%2820+%2B+30%29+=+.08
%281+%2B+3%29+%2F+50+=+.08
4+=+.08%2A50
4+=+4
OK