Susan had 117 beads and marbles altogether. The beads and marbles were either white or black. 20% of the beads and 50% of the marbles were white. There were as many black beads as black marbles.

1. Find the percentage of black beads and black marbles.

Percentage of black beads = $100\% - 20\% = 80\%$
Percentage of black marbles = $100\% - 50\% = 50\%$

2. Equate the fractions of black beads and black marbles to find the ratio of total beads to total marbles.

Since the number of black beads equals the number of black marbles:
$80\%$ of beads = $50\%$ of marbles
$\frac{4}{5}$ of beads = $\frac{1}{2}$ of marbles
$\frac{4}{5}$ of beads = $\frac{4}{8}$ of marbles
Ratio of beads to marbles = $5 : 8$

3. Compare the number of units to determine the relationship.

Since $5$ units $< 8$ units, the number of beads is fewer than the number of marbles.