Question 767060
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It is desired to draw off a part of 10 gallons of 30% solution of alcohol and to replace it by pure alcohol so as to produce a 50% solution. How many gallons should be drawn off?

Let us assume x gallons is drawn off and replaced with x gal of pure alcohol.

After drawing of x gallons of the 30% mix, what is left is (10 - x) gallons of 
30% mix.

Since it is a 30% mix, volume of alcohol in it = (10 - x)*30% = (10 - x)*0.3
= 3 - 0.3*x

After adding x gallons of pure alcohol, the total volume of the mix is again
back to 10 gallons.

In this new mix, the volume of alcohol is = original alcohol + x gallons =
(3 - 0.3*x) + x = 3 + 0.7*x

Now, this is given to be a 50% mix. i.e. ratio of alcohol in the mix is 0.5

Therefore, {{{(3 + 0.7*x) / 10 = 0.5}}}

{{{3 + 0.7*x = 5}}}
{{{0.7*x = 2}}}

{{{x = 2/0.7 = 20/7 = 2.857}}} gallons

Hope you got it :)