Let the number of $100 bills be represented by $x$. Since there are five times as many $50 bills as $100 bills, the number of $50 bills would be $5x$.

Now, we can set up an equation based on the total value of the bills:

$100x + 50(5x) = 4900$

Simplify the equation:

$100x + 250x = 4900$

$350x = 4900$

Now, solve for $x$:

$x = \frac{4900}{350} = 14$

Thus, there are 14 $100 bills.

Would you like further details or have any questions?

Here are 5 related questions:

1. How many $50 bills are there in this scenario?
2. What is the total value of the $100 bills?
3. What is the total value of the $50 bills?
4. If the total amount were increased to $9800, how many $100 bills would there be?
5. How would the number of $50 bills change if there were 10 times as many $50 bills as $100 bills?

Tip: Setting up clear equations based on variables can simplify solving word problems involving money.