There are 24 green balls and 30 red balls in a bag. What is the ratio of the number of red balls to the total number of balls?

Options

A. `5:9`
B. `12:17`
C. `14:23`
D. `23:14`

Answer

To find the ratio of the number of red balls to the total number of balls, follow these steps:

**Step 1: Identify the number of red balls.**
- The problem states that there are 30 red balls.

**Step 2: Identify the number of green balls.**
- The problem states that there are 24 green balls.

**Step 3: Calculate the total number of balls.**
- Total number of balls = Number of red balls + Number of green balls
- Total number of balls = 30 (red) + 24 (green) = 54 balls

**Step 4: Write the ratio of red balls to total balls.**
- The ratio of red balls to total balls is expressed as:
\[ \text{Ratio} = \frac{\text{Number of red balls}}{\text{Total number of balls}} = \frac{30}{54} \]

**Step 5: Simplify the ratio.**
- To simplify the ratio, find the greatest common divisor (GCD) of 30 and 54.
- The GCD of 30 and 54 is 6.
- Now divide both the numerator and the denominator by 6:
\[ \frac{30 \div 6}{54 \div 6} = \frac{5}{9} \]

**Final Answer:**
- The ratio of the number of red balls to the total number of balls is \( \frac{5}{9} \).

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