Write the shares as three parts and five parts. Since the ratio is in simplest form and both shares are whole numbers, the part size is a whole number.

The total is eight parts. Between fifty and one hundred, the possible part sizes are seven through twelve.

Five times the part size ends in zero precisely when that part size is even, giving eight, ten or twelve.

The corresponding shares are \((24,40),(30,50),(36,60)\), and these exhaust the possibilities.

Answer

\((24,40),(30,50),(36,60)\).