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

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Carcass
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The ratio, by volume, of soap to alcohol to water in a certa [#permalink] New post   23 Jul 2020, 07:28
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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
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E
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GreenlightTestPrep
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Re: The ratio, by volume, of soap to alcohol to water in a certa [#permalink] New post   23 Jul 2020, 07:53
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Carcass 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


S : A : W = 2 : 50 : 100

The solution will be altered so that the ratio of soap to alcohol is doubled
The ORIGINAL ratio is S : A = 2 : 50.
NEW ratio is S : A = 4 : 50

the ratio of soap to water is halved
The ORIGINAL ratio is S : W = 2 : 100
NEW ratio is S : W = 1 : 100


If the altered solution will contain 100 cubic centimeters of alcohol, how many cubic centimeters of water will it contain?
We need to COMBINE our two ratios.
Take S : W = 1 : 100 and create the EQUIVALENT ratio S : W = 4 : 400

We can now combine both ratios to get: S : A : W = 4 : 50 : 400
We want water = 100
So, take S : A : W = 4 : 50 : 400 and rewrite as S : A : W = 8 : 100 : 800

Answer: E

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Re: The ratio, by volume, of soap to alcohol to water in a certa [#permalink] New post   03 Feb 2021, 04:41
Hi Carcass GreenlightTestPrep

Isn't the ratio of soap to alcohol doubled means doubling both the soap and the alcohol ratio?
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Re: The ratio, by volume, of soap to alcohol to water in a certa [#permalink] New post   03 Feb 2021, 05:38
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AjanthaJ wrote:
Hi Carcass GreenlightTestPrep

Isn't the ratio of soap to alcohol doubled means doubling both the soap and the alcohol ratio?


Quote:
The solution will be altered so that the ratio of soap to alcohol is doubled
The ORIGINAL ratio is S : A = 2 : 50.
NEW ratio is S : A = 4 : 50


Just above by GreenlightTestPrep

regards
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Re: The ratio, by volume, of soap to alcohol to water in a certa [#permalink] New post   03 Feb 2021, 12:21
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AjanthaJ wrote:
Hi Carcass GreenlightTestPrep

Isn't the ratio of soap to alcohol doubled means doubling both the soap and the alcohol ratio?


Good question.
When it comes to the wording ("the ratio of soap to alcohol is doubled") of this question, it's useful to think of the ratio as a fraction

The original ratio of soap to alcohol is 2:50 (aka 2/50, aka 0.04)
So, in order to DOUBLE the ratio, our goal is to get a fraction that is TWICE the value of 2/50
In other words, we want the ratio to become 4/50

Does that help?
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Re: The ratio, by volume, of soap to alcohol to water in a certa [#permalink] New post   04 Feb 2021, 01:31
GreenlightTestPrep

Thank you sir, now it's understood.
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Re: The ratio, by volume, of soap to alcohol to water in a certa [#permalink] New post   23 Jul 2022, 05:49
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Initial ratio
Soap : alcohol : water
2 : 50 : 100

Double soap/alcohol ratio becomes 2( 2/50) which gives 4/50

Half soap/water = 1/2( 2/100) to give 2/200. To lowest term = 1/100

So new volume for soap= 4a
water = 50a
For soap and water
soap = y
Water = 100y
for soap
Y= 4a
a= y/4
Substitute for alcohol to give
50a = 12.5y
Volume of alcohol = 100cm3
so 12.5y =100
Y =8
New volume for water = 100y
Since y = 8 answer = 800.
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Re: The ratio, by volume, of soap to alcohol to water in a certa [#permalink] New post   02 Jan 2023, 23:22
OLD S:A:W = 2:50:100
OLD S/A=2/50 --> 2*S/A --> NEW S/A=4/50 --> IF NEW A=100 --> NEW S=8
OLD S/W=2/100 --> 0.5*S/W --> NEW S/W=1/100 --> SINCE NEW S=8 --> NEW W=800 --> ANSWER (E)
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Re: The ratio, by volume, of soap to alcohol to water in a certa [#permalink] New post   10 Mar 2023, 02:41
Adewale wrote:
Initial ratio
Soap : alcohol : water
2 : 50 : 100

Double soap/alcohol ratio becomes 2( 2/50) which gives 4/50

Half soap/water = 1/2( 2/100) to give 2/200. To lowest term = 1/100

So new volume for soap= 4a
water = 50a
For soap and water
soap = y
Water = 100y
for soap
Y= 4a
a= y/4
Substitute for alcohol to give
50a = 12.5y
Volume of alcohol = 100cm3
so 12.5y =100
Y =8
New volume for water = 100y
Since y = 8 answer = 800.


thanks for the methodical approach. I bolded a statement above that i believe, you meant to say "alcohol = 50a"
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Re: The ratio, by volume, of soap to alcohol to water in a certa [#permalink] New post   11 Aug 2024, 04:35
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