Data, Statistics & Probability · Hard problem

A survey asked $25$ families how many pets they own. The results were: $0$ pets, $6$ families; $1$ pet, $8$ families; $2$ pets, $5$ families; $3$ pets, $4$ families; $4$ pets, $2$ families. How many more families, each owning exactly $4$ pets, would have to join the survey to make the mean number of pets per family exactly $2$?