OG 13 200

oquiella 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 contai 100 cubic centtimeters of alcohol, how many cubic centtimeters of water will it contain?

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


Answer: E


PLease explain in lamest terms.

The ratio S:A:W is 2:50:100. The ratio S:A when doubled becomes 2S:A or 4:50 in this case, and when the ratio S:W is halved, it becomes S:2W or 2:200 in this case. Soap is common in the two ratios, in first it’s 4 and in the other, it is 2, so take 4 for soap ratio everywhere. We therefore need to multiply contents in 2:200 by 2 to get 4:400.

The resulting ratio S:A:W is 4:50:400.

Hence, when the altered solution contains 50 cubic centimeters of alcohol, it contains 400 cubic centimeters of water; similarly, when the altered solution contains 100 cubic centimeters of alcohol, it will contain [spoiler]800 cubic centimeters of water.

Take E[/spoiler].