To solve this, let’s define the variables:

• Let $r$ represent the number of red marbles.
• Let $b$ represent the number of black marbles.

According to the problem, the total number of marbles is 120:

$r + b = 120$

Additionally, there are 19 red marbles for every black marble. This gives us the ratio:

$r = 19b$

Now, substitute $r = 19b$ into the first equation:

$19b + b = 120$

Combine the terms:

$20b = 120$

Solve for $b$:

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

Now that we know there are 6 black marbles, substitute $b = 6$ into the equation for $r$:

$r = 19 \times 6 = 114$

So, there are 114 red marbles in the bag.

Would you like more details or have any questions?

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Here are 5 related questions to explore further:

1. If there were 130 marbles in the bag, how many would be red?
2. What is the total weight of the marbles if each red marble weighs 5g and each black marble weighs 7g?
3. If 5 red marbles were removed, what would be the new ratio of red to black marbles?
4. If the ratio of red to black marbles was 10:1 instead of 19:1, how many red marbles would be in the bag?
5. How would the answer change if the total number of marbles was 150 instead of 120?

Tip: When solving ratio problems, expressing one variable in terms of the other helps simplify the equation.