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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.

Respuesta :

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:

[tex]\frac{3}{5}\left(x-\frac{1}{4}x-\frac{1}{8}x\right)=15[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:}5[/tex]

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

[tex]3(\frac{8x-2x-x}{8}) =75[/tex]

[tex]3(\frac{5x}{8}) =75[/tex]

Dividing both sides by 3.

[tex]\frac{5x}{8} =25[/tex]

Multiplying both sides by 8, we get

5x = 200.

Dividing both sides by 5, we get

x= 40.

Therefore, 40 students were surveyed.



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