Question

Students were surveyed about their favorite colors. 1/4 of the students preferred red. 1/8 preferred blue. 3/5 of the remaining students preferred green. If 15 students preferred green, how many students were surveyed?

Answer 1

Answer:

30 students were surveyed

Step-by-step explanation:

let the total students be x

the students who preferred red = 1/4 x

the students who preferred blue = 1/8 x

∴the remaining students = x-(1/4 x + 1/8 x)

                                         = x - (3/8 x)

                                         =  5/8 x

∴3/5 of 5/8 x = 3/5 × 5/8 x = 3/8 x

hence, 3/8 x students preferred green

∴  3/8 x = 15

or, 3x    = (15×8)

or,  x     = (5×8)  = 40

∴numbers of students who were surveyed = {(1/4)×40} + {(1/8)×40} + 15

                                                                       =  10+5+15  

                                                                       =    30