How much 90 percent vinegar do you have to add to a gallon of 5 percent vinegar to get 20 percent vinegar?

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How much 90 percent vinegar do you have to add to a gallon of 5 percent vinegar to get 20 percent vinegar?

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Answer 1 · 2017-01-25T12:41:26

$\frac{3}{14} g a l l o n$ $3/14 gallon$ of $90 %$ $90%$ vinegar to be added to get $20 %$ $20%$ vinegar.

Explanation:

Let $x$ $x$ gallons of $90 %$ $90%$ vinegar is added to get $20 %$ $20%$ vinegar.

Then by given condition , $1 \cdot \frac{5}{100} + x \cdot \frac{90}{100} = (1 + x) \cdot \frac{20}{100} or \frac{1}{20} + \frac{9}{10} x = \frac{1}{5} + \frac{1}{5} x or \frac{9}{10} x - \frac{1}{5} x = \frac{1}{5} - \frac{1}{20} or \frac{7}{10} x = \frac{3}{20} or x = \frac{10 \cdot 3}{7 \cdot 20} = \frac{3}{14} g a l l o n$ $1*5/100 + x*90/100= (1+x)*20/100 or 1/20+ 9/10x = 1/5 + 1/5x or 9/10x - 1/5x = 1/5-1/20 or 7/10x=3/20 or x = (10*3)/(7*20)= 3/14 gallon$

$\frac{3}{14} g a l l o n$ $3/14 gallon$ of $90 %$ $90%$ vinegar to be added to get $20 %$ $20%$ vinegar.[Ans]

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How much 90 percent vinegar do you have to add to a gallon of 5 percent vinegar to get 20 percent vinegar?

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