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Re: The ratio, by volume, of soap to alcohol to water in a certa [#permalink]
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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

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Re: The ratio, by volume, of soap to alcohol to water in a certa [#permalink]
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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]
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]
2
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]
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]
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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