Let the number of black marbles be $x$.

Since there are 19 red marbles for every black marble, the number of red marbles would be $19x$.

The total number of marbles is the sum of red and black marbles, which gives:

$x + 19x = 120$

Simplifying the equation:

$20x = 120$

Now, solve for $x$:

$x = \frac{120}{20} = 6$

Therefore, the number of black marbles is $6$.

Since the number of red marbles is $19x$, we have:

$19 \times 6 = 114$

Thus, there are 114 red marbles in the bag.

Would you like more details or have any questions? Here are 5 related problems to consider:

1. What if the ratio of red to black marbles was 3:1 instead of 19:1?
2. How many black marbles are in the bag?
3. If 10 more black marbles are added, how many total marbles will the bag contain?
4. What is the percentage of red marbles in the bag?
5. If 5 red marbles were removed, how many would remain?

Tip: When working with ratios, think of one quantity as a multiple of the other to set up the equation easily.