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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
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How many liters of 20% vinegar solution should be added to 4
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04 Dec 2020, 06:23
04 Dec 2020, 06:23
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How many liters of 20% vinegar solution should be added to 4 liters of 50% vinegar solution to make a 30% vinegar solution?
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8
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: How many liters of 20% vinegar solution should be added to 4
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04 Dec 2020, 06:32
04 Dec 2020, 06:32
GreenlightTestPrep wrote:
How many liters of 20% vinegar solution should be added to 4 liters of 50% vinegar solution to make a 30% vinegar solution?
Show: ::
8
When solving mixture questions, it can be useful to sketch the solutions with the ingredients SEPARATED.
50% of 4 liters = 2 liters. So, the original mixture contains 2 liters of vinegar
Let x = the volume (in liters) of 20% solution required
So, this solution contains 0.2x liters of vinegar
We get:
We want the resulting solution to be 30% vinegar .
In other words, we want: \(\frac{2 + 0.2x}{4+x}=\frac{3}{10}\) (aka 30%)
Cross multiply: \((10)(2 + 0.2x) = 3(4+x)\)
Expand: \(20 + 2x = 12+3x\)
Solve: \(x = 8\)
Answer: 8
Cheers,
Brent
gmatclubot
Re: How many liters of 20% vinegar solution should be added to 4 [#permalink]
04 Dec 2020, 06:32
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