# How much of 30% solution of alcohol and how much of a 70% solution should be mixed to give 30 gallons of 60% solution?

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by gendoy11

2015-09-26T22:42:51+08:00

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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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