1/4 of students prefer red, 1/8 of students prefer blue, and 3/5 of remaining students prefer green. if 20 students prefer green how many students are there?

Number of students preferring red = x/4
Number of students preferring blue = x/8
Then
Number of students remaining = x - [(x/4) + (x/8)]
                                                   =x - [(2x + x)/8)
                                                   = x - (3x/8)
                                                   = (8x - 3x)/8
                                                   = 5x/8
Number of students preferring the color green = (3/5) * (5x/8)
                                                                           = 3x/8
We also know that the total number of students preferring the color green is 15.   So..
3x/8 = 15
3x = 15 * 8
x = (15 * 8)/3
   = 5 * 8
   = 40
So the total is 40 students