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