Question

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

Answer 1

Let us assume the total number of students surveyed = x

Then

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 in total 40 students were surveyed. I hope the procedure is clear to you.

Explanation: