We can solve this question using cross multiplication,
If the number of students who sleep 6 hours a day increases by, this means we'll have a total of 6 students who sleep 6 hours a day.
We want the ratio to be same: 15%
Then we can write:
[tex]\frac{6}{N}=\frac{15\%}{100\%}[/tex]
6 students are the 15%, then N students are the 100%
Now solve for N:
[tex]\begin{gathered} 6·100=15·N \\ \end{gathered}[/tex][tex]N=\frac{600}{15}[/tex][tex]N=40[/tex]
The answer is 40 students are expected.
This is a reasonable answer, given that if the number of students who sleep 6 hours doubles, for the rate to remain the same, the total of students must double.
