Question 272438: How many ounces of a 20% alcohol solution must be mixed with 15 ounces of a 25% alcohol solution to make a 23% alcohol solution?
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! In solving "solutions" problems, you have to keep track of the amount of pure stuff you need at the end.
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x = ounces of 20% alcohol solution to add to the 15 oz of 25% solution
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15 oz of a 25% solution = 3.75 oz of pure alcohol
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The total amount can be described 15+x ounces.
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We solve the problem in terms of the amount of pure alcohol
.2x + 3.75 = .23(15+x)
.2x + 3.75 = 3.45 + .23x
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Subtracting .2x from both sides
3.75 = .03x + 3.45
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Subtracting 3.45 from both sides
.3 = .03x
Multiply by 100
30 = 3x
Divide by 3
10 = x
x = 10
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So, you have to add 10 oz of 20% alcohol solution to 15 oz of 25% alcohol.
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Always check your work.
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At the end we would have 25 oz that we believe would be 23% alcohol. If that is true, then we would have:
.23 * 25 = 5.75 oz of pure alcohol in the solution.
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We have shown (above) that we have 3.75 oz of pure alcohol in the 15 oz of 25% solution.
How many oz of pure alcohol is there in 10 oz of 20% alcohol?
.2*10 = 2 oz
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3.75 + 2 = 5.75 oz, which is exactly what we needed
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check the question to be sure you answer it at the end...
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How many ounces do you need to add?
You need to add 10 ounces of 20% alcohol solution.
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