There are 136 students in the cafeteria. the ratio of students buying lunch to those who brought their lunch is 3: 1. how many students brought their lunch?

If the ratio of students who are buying lunch to those who bought their lunch are 3:1.  This means that for every 3 students that buy their lunch, there is 1 student who brings their lunch.  This allows us to create the following equation:

3x + 1x = 136

To solve this equation, we must first combine like terms on the left side of the equation, which gives us:

4x = 136

Finally, we should divide both sides of the equation by the coefficient of the variable x, which is 4:

x = 34

We know that the number of students that brought their lunch is represented by the expression 1x.  Therefore, 34(1), or 34 students brought their lunch.

Hope this helps! :)