Students were surveyed about their favorite colors one fourth of the students preferred red 1/8 of the students preferred blue, and3/5 of the remaining students preferred green. If 15 students prefer green how many students were surveyed

Question

Mathematics

Yadiel Mata

21 January, 07:34

Students were surveyed about their favorite colors one fourth of the students preferred red 1/8 of the students preferred blue, and3/5 of the remaining students preferred green. If 15 students prefer green how many students were surveyed

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Answers (1)

Know the Answer?

Koen Joyce · 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.