In the question below, it is asked for the minimum number of students who have failed in one or more subjects(Please correct me if I am wrong). This gives us (Max possible number of students to fail in only one subject)+(Minimum possible number of students failed in two or more subjects)=45.

In the solution the above equation is given by a+6f=45.

How can 'a' be 29(for 'f'=13) if the maximum number of students failed in a subject = 22(Maths)?