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.

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:

" alt="5\cdot \frac{3}{5}\left(x-\frac{1}{4}x-\frac{1}{8}x\right)=15\cdot \:5" />" />

Dividing both sides by 3.

Multiplying both sides by 8, we get

5x = 200.

Dividing both sides by 5, we get

x= 40.

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.