Each light bulb at a hotel is either incandescent or fluorescent. At a certain moment, thirty percent of the incandescent bulbs are switched on, and eighty percent of the fluorescent bulbs are switched on. If 70 percent of all the bulbs are switched on at this moment, what percent of the bulbs that are switched on are incandescent?  Choose the correct answer:  A) 4.5 %  B) 8.6 %  C) 12.3 %  D) 16.7 %  E) 20 %

Rationale: let i be the number of incandescent bulbs . let f be the number of fluorescent bulbs . 0.3 i + 0.8 f = 0.7 ( i + f ) 0.1 f = 0.4 i f = 4 i this means that for every 1 incandescent bulb , there are 4 fluorescent bulbs . the percent of bulbs that are switched on which are incandescent is : 0.3 i / ( 0.3 i + 0.8 f ) = 0.3 i / ( 0.3 i + 0.8 * 4 i ) = 0.3 i / 3.5 i = 3 / 35 which is about 8.6 % . the answer is b .
Answer: B