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The ratio, by volume, of soap to alcohol to water in a
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Updated on: 26 Apr 2012, 08:25
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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?
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?
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
Please explain answers, shortcuts, etc. Thanks!!
soap:alcohol Intial ratio soap:alcohol: water --> 2:50:100 Inital soap:alcohol = 2/50 =2:50 after doubled soap:alcohol =2* 2/50 = 4:50
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?
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?
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 \(w=2*400=800\).
Answer: E.
How you get 1/100=4/400?? Why you multiply by 4??
We have that s/a=4/50 (s corresponds to 4) and s/w=1/100 (s corresponds to 1). To get s/a/w ratio we need s to correspond to the same number in both ratio, so we multiply 1/100 by 4 to get s/w=4/100.
_________________
Re: The ratio, by volume, of soap to alcohol to water in a
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20 Jan 2015, 05:28
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I am using the unknown mupltiplier method for 3 quantities for such problems.
Initial ratios: S:A:W 2:50:100
From stem: (2/50)2=4/50= 2/25 (2/100)/2=2/200=1/100
Then we use the above mentioned approach like this:
S___A___W 2__25___W --> This is the new ratio for S and A 1__A___100--> This is the new ration for S and W
What we need to do now is create a common denominator for S, as we have 2 different values: LCM of 1 and 2 is 2, so we multiply the first row by 1 (since it already is 2) and the second row by 2 (since it is 1):
S___A___W--->S___A___W 2__25___W --->2__25___W (*1) 1__A___100--->2__25__200 (*2). A just goes down because there was no value there are we already have this ratio.
Now normally you would have the amount for the whole such as this:
S___A___W__ 2x+25x+200x= the given amount.
Now we have that 25x=100-->x=4 Then 200x = 200*4=800. ANS E
Re: The ratio, by volume, of soap to alcohol to water in a
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30 Dec 2015, 10:20
x2suresh 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
Please explain answers, shortcuts, etc. Thanks!!
soap:alcohol Intial ratio soap:alcohol: water --> 2:50:100 Inital soap:alcohol = 2/50 =2:50 after doubled soap:alcohol =2* 2/50 = 4:50
Re: The ratio, by volume, of soap to alcohol to water in a
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22 Jan 2016, 09:01
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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?
Re: The ratio, by volume, of soap to alcohol to water in a
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13 Jul 2016, 06:32
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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
The first thing we want to do is set up the ratio of the original solution using variable multipliers.
soap : alcohol : water = 2x : 50x : 100x
We are given that the ratio of soap to alcohol is doubled. Our original ratio of soap to alcohol is:
soap/alcohol = 2x/50x = x/25x
(Notice that we only canceled the 2 and 50; we didn’t cancel the x because it’s our ratio multiplier.)
If we double the ratio we multiply the entire ratio by 2, so we have:
2(x/25x) = 2x/25x
So now our new ratio is:
soap/alcohol = 2x/25x
Next we are given that the ratio of soap to water is halved. Our original ratio of soap to water is:
soap/water = 2x/100x = x/50x
If we halve the ratio, we multiply the entire ratio by 1/2, so we have:
(1/2)(x/50x) = x/100x
So now our new ratio is:
soap/water = x/100x
Next we must notice that the amount of soap in the two new ratios is not the same value. In the first new ratio, soap = 2x and in the second new ratio, soap = x. Thus, we need to make these values equal before continuing to the answer. To do this, we multiply the second ratio by 2/2, so we have:
soap/water = (2/2)(x/100x) = 2x/200x
Now we can set up the ratio of the altered solution.
soap : alcohol : water = 2x : 25x : 200x
Lastly, we are given that the altered solution will contain 100 cubic centimeters of alcohol.
With this we can set up the following equation and determine x:
25x = 100
x = 4 (This means that the ratio multiplier is 4.)
Thus, the altered solution will contain (200)(4) = 800 cubic centimeters of water.
Re: The ratio, by volume, of soap to alcohol to water in a
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20 Jul 2016, 18:58
Top Contributor
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
soap:alcohol is doubled implies the ratio is 4:50:100 Also, soap :water is halved implies the ratio is 4:50:400 So when alcohol is 100 cubic cm, water is 800 cubic cm.
_________________
Re: The ratio, by volume, of soap to alcohol to water in a
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24 Jun 2017, 02:19
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I think this problem can be solved with accuracy by setting up a table. Please see the attached table. The table is self explanatory. Let know if an explanation needed.
Answer = 800
option E
Attachments
OG13_Problem 200.png [ 24.13 KiB | Viewed 27320 times ]
Re: The ratio, by volume, of soap to alcohol to water in a
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24 Dec 2017, 11:15
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
S:A:W=2:50:100 =>S/A=2x/50x --- new ratio =4x/50x =>S/W=2x/100x -- new ratio =x/100x
So, A/S=50x/4x and, W/S=100x/x or 400x/4x
Therefore, new S:A:W=4:50:400 Now A=100 =>50x=100 =>x=2
The ratio, by volume, of soap to alcohol to water in a
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02 Nov 2018, 10:36
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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
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