Problem: the ratio , by volume , of soap to alcohol to water in a certain solution is 4 : 20 : 60 . 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 ?
Rationale: "soap : alcohol initial ratio soap : alcohol : water - - > 4 : 20 : 60 initial soap : alcohol = 4 / 20 = 4 : 20 after doubled soap : alcohol = 2 * 4 / 20 = 8 : 20 initial soap : water = 4 / 60 = 4 : 60 after halved soap : water : 1 / 2 * 4 / 60 = 2 / 60 = 2 : 60 after soap : alcohol : water - - > 8 : 20 : 240 - - > 2 : 5 : 60 given alcohol 100 cubic centimeter . ratio is 40 : 100 : 1200 ( 2 : 5 : 60 ) for 100 cubic centimeter of alcohol - - - 1200 cubic cm water is required ."
annotated_formula: divide(divide(divide(divide(divide(volume_rectangular_prism(100, 60, 20), const_3), const_2), 4), 4), 4)