Using the variables we assigned earlier and the given information, we can expressed the number of the four groups as:
We know that the sum of the numbers for these four groups should equal to the total number of pupils in the class, hence we have:
which simplifies to . Now we need to do a little analysis, in order to make to be as large as possible, we need the product to be as small as possible. We know and , it is hard to just randomly pick the percentages and here, so lets assume both , we got . However this can not be true, since both percentages need to be strictly greater than , so the largest possible number of pupils in the class will be .