KöMaL 2014 K430

Consider the notation $33335 = 3_{4}5_{1}$, that is, the number in the subscript denotes the number of identical digits next to each other (the numbers in the subscripts must be positive integers). Determine the values of the letters in the expression $1_{x}4_{y}3_{z}8_{w}+ 4_{p}8_{q}3_{r} = 5_{2}9_{3} 7_{3}2_{2} 1_{1}$.