let 'x' be the amount of solution at 30%
let 'y' be the amount of solution at 70%
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Adding both you'll have 30 gallons of 60% solution
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Getting the value of alcohol in the mixture we'll have:
0.3x + 0.7y = 0.6(30gal)
0.3x + 0.7y = 18gal -------equation1
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Since the total mixture amounts to 30 gal then
x + y = 30 ----equation 2
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From equation 2
x = 30 - y -----equation 2'
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Substitute equation 2' to equation 1
0.3x + 0.7y = 18
0.3(30 - y) + 0.7y = 18
9 - 0.3y + 0.7y = 18
-0.3y + 0.7y = 18 - 9
0.4y = 9
y = 22.5 gal
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Substitute y = 22.5 to equation 2'
x = 30 - y
x = 30 - 22.5
x = 7.5 gal
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