Finding the number of chairs

Question

In a school hall, $7/31$ of chairs is arranged in rows of 5, $11/31$ of chairs is arranged in rows of 13. The rest of chairs are not used. The total number of chairs does not exceed 4000. Find the number of chairsAttempts:

$x= 31k$

since 31 is the denominator and also a prime

$7/31*x=5l$

$x=155/7*l$

since it is arranged in rows of 5

$11/31*x=13j$

$x=403/11*j$

since it is arranged in rows of 13

Am I approaching this wrongly? And if i am approaching the right way, how can i continue?

Answer 1

Hint: note that your $x$ will be divisible by $403$ and $155$ (Why?). Try to argue now what number $x$ can be assuming $x \leq 4000$.