Question

Students were surveyed about their favorite colors. 1/4 of the students preferred red, 1/8 of the students preferred blue, and 3/5 of the remaining students chose green. If 15 students preferred green, how many students were surveyed? What operations are needed to solve? Show all work. Justify or explain answer.

Answer 1

Let us assume total number of students were surveyed = x.

1/4 of x students preferred red = 1/4 x.

1/8 of of x students preferred blue = 1/8 x

Remaining students = (x - 1/4 x - 1/8 x)

3/5 of the remaining students chose green that is 3/5 of (x - 1/4 x - 1/8 x).

15 students preferred green.

So, we can setup an equation:

`(3)/(5)\left(x-(1)/(4)x-(1)/(8)x\right)=15`

`\mathrm{Multiply\:both\:sides\:by\:}5`

`[tex]5\cdot (3)/(5)\left(x-(1)/(4)x-(1)/(8)x\right)=15\cdot \:5`[/tex]

`3((8x-2x-x)/(8)) =75`

`3((5x)/(8)) =75`

Dividing both sides by 3.

`(5x)/(8) =25`

Multiplying both sides by 8, we get

5x = 200.

Dividing both sides by 5, we get

x= 40.

Therefore, 40 students were surveyed.