Question

how would you put this into a multiplication 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 preferred green.

If 15 students preferred green, how many students were surveyed?

Answer 1

Step-by-step explanation:

1/4 + 1/8 = 2/8+1/8 = 3/8 , the remaining students is therefore 1 - 3/8 = 8/8 - 3/8 = 5/8

3/5 of this remaining students is 3/5 of 5/8 or 3/5×5/8 = 3/8

If 3/8 of the surveyed class is equal to 15 then the whole class size is equal to 15 divided by 3/8 or 15×8/3 = 40

Therefore the answer is 40 students

remember, when dividing by a fraction you invert the fraction and multiply.

Hope it is helpful

Answer 2

Answer:

40 students were surveyed

Step-by-step explanation:

$\frac{1}{4}$ + $\frac{1}{8}$ = $\frac{3}{8}$ of the students preferred red and blue

1 - $\frac{3}{8}$ = $\frac{5}{8}$ is the part of the remaining students

$\frac{5}{8}$ × $\frac{3}{5}$ = $\frac{3}{8}$ of the students preferred green

If "s" is total amount of students, then

$\frac{3}{8}$ × s = 15 ⇒ s = 15 ÷ $\frac{3}{8}$ ⇒ s = $\frac{15*8}{3}$ = 40 students were surveyed.

==========

Check the answer:

40 × $\frac{1}{4}$ = 10 students preferred red

40 × $\frac{1}{8}$ = 5 students preferred blue

( 40 - 15) × $\frac{3}{5}$ = 15 students preferred green