# Question Regarding a Class of Students

A class has less than 30 students.

1. Exactly 3/4 of them own footballs.
2. Exactly 7/8 of them own football boots.

i.How many students are there in the class?

ii.How many students own both football boots and footballs?

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There is not enough information: the number could be any of $8$, $16$, or $24$. –  André Nicolas Dec 16 '12 at 18:38

Take the number of students as $x<30$ and take $y$ as the number of students with both football and football boots, then form your equations
• $\cfrac 34 x$ own footballs
• $\cfrac 78x$ own football boots
• $\cfrac 34x + \cfrac 78x -y = x \iff 5x-8y=0$
Solve the last equation for non negative integer values of $x$ and $y$ less than $30$