SOLUTION: how much pure (100%) vinegar and 5% vinegar must be mixed to obtain 50oz of a 24% solution

Question 519853: how much pure (100%) vinegar and 5% vinegar must be mixed to obtain 50oz of a 24% solution
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
With mixture or solutions you need to keep track of how much pure stuff you need or have.
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You are to make 50 oz of 24% solution, so it will have 50*.24 = 12 oz of pure vinegar.
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You have 100% (pure) vinegar and 5% vinegar to mix together.
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x = amount of pure vinegar
y = amount of 5% vinegar
x +y = 50
y = 50-x
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x + .05(50-x) = 12
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multiply by 100 to eliminate decimals
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100x + 5(50-x) = 1200
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100x +250 -5x = 1200
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95x = 950
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x = 10 oz of pure vinegar
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y = 50-10
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y = 40 oz of 5% vinegar
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Answer: Mix 10 oz of pure vinegar and 40 oz of 5% vinegar to produce 50 oz of 24% vinegar.
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Check the pure stuff to be sure the answer is correct.
10 oz pure vinegar + .05(40) = 12 oz
.24*50 = 12 oz
So, 12 oz of pure vinegar in 50 oz solution is as 24% solution.
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Done.
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