In order to calculate the total number of students, we have that if 24% of the students purchased lunch, the other 76% brought lunch from home, and that percentage corresponds to 190 students.
Then, using a rule of three, we have:
[tex]\begin{gathered} 76\text{\%}\to190\text{ students} \\ 100\text{\%}\to x\text{ students} \\ \\ \frac{76}{100}=\frac{190}{x} \\ 76x=19000 \\ x=\frac{19000}{76} \\ x=250 \end{gathered}[/tex]So the total number of students is 250.