Higher Paper 2

\begin{aligned} &\text{Vicky has a collection of medals. The Venn diagram gives information about the numbers of medals, where}\\ &\mathcal{E}=\{\text{all medals}\},\; A=\{\text{English medals}\},\; B=\{\text{gold medals}\}.\\[2mm] &\text{The regions are labelled } 7x-13\; (A\setminus B),\; x\; (A\cap B),\; 4x-6\; (B\setminus A),\; 31\; (\mathcal{E}\setminus (A\cup B)).\\[2mm] &\text{Given that a medal is gold, } P(\text{English})=\tfrac{2}{9}.\\[1mm] &\text{Work out the total number of medals in Vicky's collection.} \end{aligned}