a bag contains 120 marbels some are red the rest are black there are 19 marvels red marvels for every black marble how many red marvels are in the bag

Let's solve the problem step by step.

Let:
- \( r \) be the number of red marbles,
- \( b \) be the number of black marbles.

According to the problem, the ratio of red marbles to black marbles is \( 19:1 \), meaning there are 19 red marbles for every black marble. This gives the relation:

\[
r = 19b
\]

Also, the total number of marbles is 120:

\[
r + b = 120
\]

Now, substitute \( r = 19b \) into the total equation:

\[
19b + b = 120
\]

Simplify:

\[
20b = 120
\]

Solve for \( b \):

\[
b = \frac{120}{20} = 6
\]

Now, substitute \( b = 6 \) back into the equation \( r = 19b \):

\[
r = 19 \times 6 = 114
\]

So, there are **114 red marbles** in the bag.

Would you like more details, or do you have any questions?

Here are 5 related questions for further exploration:
1. How many black marbles are in the bag?
2. What would happen if there were 150 marbles in total instead of 120?
3. What if the ratio was 5:1 instead of 19:1?
4. How would the number of marbles change if the total was increased by 50%?
5. What if 20% of the black marbles were removed from the bag?

**Tip**: Always check your equations by plugging the numbers back into the original conditions to ensure accuracy.

A bag contains 120 marbles, some are red, the rest are black. There are 19 red marbles for every black marble. How many red marbles are in the bag?

Find out how to calculate the number of red marbles in a bag with 120 total marbles and a 19:1 ratio of red to black marbles. This problem uses ratios and linear equations, making it ideal for students in Grades 6-8.

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