Let p represent the number of purses in Sharon's collection. We can write an expression to represent the number of purses in Sharon's collection as: p = 4 + (1/3)p.
To find the number of purses in Sharon's collection, substitute 15 for p in the expression and solve for p. This gives us: p = 4 + (1/3)(15) = 19.
Therefore, Sharon has 19 purses in her collection.