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The ratio, by volume, of soap to alcohol to water in a

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Intern
Joined: 29 Sep 2018
Posts: 11
Re: The ratio, by volume, of soap to alcohol to water in a  [#permalink]

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11 Nov 2018, 12:41
First, double the ratio of soap to alcohol (2:50):

Original: $$\frac{2}{50}$$

Double:$$\frac{2}{50} * \frac{2}{1} = \frac{4}{50}$$

Next, halve the ratio of soap to water (2:100):

Original: $$\frac{2}{100}$$

Halve: $$\frac{2}{100} * \frac{1}{2} = \frac{2}{200}$$

Multiply 2/200 by 2/2 to give soap a value of 4 in both ratios:

$$\frac{2}{200} * \frac{2}{2} = \frac{4}{400}$$

Combine the ratios, using soap as the common value:

$$Soap:Alcohol:Water = 4:50:400$$

Use equivalent ratio to find value of water for given quantity of alcohol:

$$\frac{Water}{Alcohol} = \frac{400}{50}$$

Set equivalent to known value of alcohol:

$$\frac{400}{50} = \frac{w}{100}$$

$$\frac{(100*400)}{50} = w$$

$$800 = w$$ (answer: E)
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Joined: 01 Jan 2019
Posts: 107
Concentration: Finance, Entrepreneurship
GPA: 3.24
Re: The ratio, by volume, of soap to alcohol to water in a  [#permalink]

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06 Sep 2019, 19:38
Bunuel wrote:
droopy57 wrote:
The ratio, by volume, of soap to alcohol to water in a certain solution is 2:50:100. The solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved. If the altered solution will contain 100 cubic centimeters of alcohol, how many cubic centimeters of water will it contain?

(a) 50
(b) 200
(c) 400
(d) 625
(e) 800

Given: $$\frac{s}{{\frac{a}{w}}}=\frac{2}{{\frac{50}{100}}}$$;

The ratio of soap to alcohol is doubled --> $$\frac{s}{a}=2*\frac{2}{50}=\frac{4}{50}$$;

The ratio of soap to water is halved --> $$\frac{s}{w}=\frac{1}{2}*\frac{2}{100}=\frac{1}{100}=\frac{4}{400}$$;

New ratio: $$\frac{s}{{\frac{a}{w}}}=\frac{4}{{\frac{50}{400}}}$$ --> $$\frac{a}{w}=\frac{50}{400}$$ --> if $$a=2*50=100$$ then $$w=2*400=800$$.

Bunuel,
I am stuck... The part of stem which says the ratio of s:w is halved, so s:w is 2:100 and when halved, I got it 1:50. Why can’t this be correct? I don’t understand where am I faltering?

Posted from my mobile device
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Joined: 23 Feb 2015
Posts: 1947
Re: The ratio, by volume, of soap to alcohol to water in a  [#permalink]

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19 Apr 2020, 20:46
mgoblue123 wrote:
The ratio, by volume, of soap to alcohol to water in a certain solution is 2:50:100. The solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved. If the altered solution will contain 100 cubic centimeters of alcohol, how many cubic centimeters of water will it contain?

A. 50
B. 200
C. 400
D. 625
E. 800

Let,
S=2x
A=50x
W=100x

If altered:
S:A=$$\frac{2x}{50x}*2$$
-->$$\frac{4x}{50x}$$

S:W=$$\frac{2x}{100x*2}$$
-->$$\frac{x}{100x}$$
-->$$\frac{4x}{400x}$$ (equating both soap mixed multiplying by 4)

So, the altered solution is:
S:A:W=$$4x:50x:400x$$

Here,
$$50x=100$$
-->$$x=2$$
So, water $$(W)=400x$$
$$=400*2$$
$$=800$$
The correct choice is E
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Joined: 23 Feb 2015
Posts: 1947
The ratio, by volume, of soap to alcohol to water in a  [#permalink]

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19 Apr 2020, 20:58
Shef08 wrote:
Bunuel wrote:
droopy57 wrote:
The ratio, by volume, of soap to alcohol to water in a certain solution is 2:50:100. The solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved. If the altered solution will contain 100 cubic centimeters of alcohol, how many cubic centimeters of water will it contain?

(a) 50
(b) 200
(c) 400
(d) 625
(e) 800

Given: $$\frac{s}{{\frac{a}{w}}}=\frac{2}{{\frac{50}{100}}}$$;

The ratio of soap to alcohol is doubled --> $$\frac{s}{a}=2*\frac{2}{50}=\frac{4}{50}$$;

The ratio of soap to water is halved --> $$\frac{s}{w}=\frac{1}{2}*\frac{2}{100}=\frac{1}{100}=\frac{4}{400}$$;

New ratio: $$\frac{s}{{\frac{a}{w}}}=\frac{4}{{\frac{50}{400}}}$$ --> $$\frac{a}{w}=\frac{50}{400}$$ --> if $$a=2*50=100$$ then $$w=2*400=800$$.

Bunuel,
I am stuck... The part of stem which says the ratio of s:w is halved, so s:w is 2:100 and when halved, I got it 1:50. Why can’t this be correct? I don’t understand where am I faltering?

Posted from my mobile device

Shef08
ratio of s:w is halved means you need to divide the ''ratio'' by 2 ($$\frac{2}{100×2}$$=$$\frac{1}{100}$$). But, you are dividing ''every parts'' of a ''ratio''.
The ratio, by volume, of soap to alcohol to water in a   [#permalink] 19 Apr 2020, 20:58

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