Question

How many ounces of pure alcohol should be added to 500 ounces of 35 % alcohol solution to produce a solution that is 50 %?

Pesent your answer as an integer or a reduced fraction. Do not use decimals.

Answer 1

150 ounces

Explanation:

It is convenient to write an equation for the total amount of alcohol in the mix.

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Let x represent the amount of pure alcohol added. Then the amount of alcohol in the mix is ...

500(35%) +x(100%) = (500 +x)(50%)

x = 500(15%) +x(50%) . . . . . . . subtract 500(35%)

x(50%) = 500(15%) . . . . . . . . . . subtract x(50%)

x = (500)(15%)/(50%) = 150 . . . . divide by the coefficient of x

150 ounces of pure alcohol should be added to produce the desired solution.