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

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.

Learn how to solve a ratio-based word problem involving a total of 120 marbles, where there are 19 red marbles for every black marble. The solution includes using algebraic equations to find the number of red marbles. Suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation