In front of our school, there is a flower bed. One fifth of all the flowers are tulips, two ninths are daffodils, four fifteenths are hyacinths, and the rest are pansies. How many flowers are there in total in the bed if there are no more than 60 and no fewer than 30 of any type? (M. Petrová)

Hint. Could there be, for example, 100 flowers in the bed?