It's possible that the expected answer is something like sampling some percentage of each class, but I'm not sure.
As I see it, you need to take some sort of sample just to find out who eats breakfast, so I'm not sure you can just put those who do and those who don't into different groups before choosing whose grades to look at.
And as I understand it, stratified sampling is used just to make sure everyone is counted equally, not to compare two strata.
But I'm not a statistician, so I'm not sure.