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!!
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 \(w=2*400=800\).
Answer: E.
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?