Solution

23217

First name
Fionn Bishop
School
Thomas Hardye School
Country
Age
14

The word document entered below shows my method of working out the unknowns in the arithmagons.

It is impossible to have integers on the edges and fractions on the vertices. If you have two integers, x=m/1 and y=n/1, when you multiply them, it will be pq/1, which is an integer.

In the same way, it is impossible to have rational numbers on the edges and irrational vertices.