Simultaneous Equations - Application of Simultaneous Equations in Real World Contexts

A fraction \(\dfrac{p}{q}\) is such that when \(5\) is added to its numerator, the fraction becomes \(\dfrac23\).
One quarter of the sum of the numerator and denominator is \(5\).

1. Write down two equations relating \(p\) and \(q\).

   [2]

2. Solve the simultaneous equations and find the original fraction.

   [4]