A bag contains x red balls, (x + 5) blue balls and (3x + 10) white balls. If the probability of drawing a blue ball is `2/9`, what is the number of white balls?

Options

A. 15
B. 20
C. 35
D. 55

Answer

To solve the problem step by step, we will follow the reasoning presented in the video transcript.

### Step 1: Define the number of balls
We have:
- Red balls = \( x \)
- Blue balls = \( x + 5 \)
- White balls = \( 3x + 10 \)

### Step 2: Calculate the total number of balls
The total number of balls in the bag can be calculated by adding the number of red, blue, and white balls:
\[ \text{Total balls} = x + (x + 5) + (3x + 10) \]
Simplifying this gives:
\[ \text{Total balls} = x + x + 5 + 3x + 10 = 5x + 15 \]

### Step 3: Set up the probability equation
The probability of drawing a blue ball is given as \( \frac{2}{9} \). The probability formula is:
\[ \text{Probability} = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} \]
Here, the favorable outcomes are the blue balls, which is \( x + 5 \). Therefore, we can set up the equation:
\[ \frac{x + 5}{5x + 15} = \frac{2}{9} \]

### Step 4: Cross-multiply to solve for \( x \)
Cross-multiplying gives:
\[ 9(x + 5) = 2(5x + 15) \]
Expanding both sides:
\[ 9x + 45 = 10x + 30 \]

### Step 5: Rearranging the equation
Now, we rearrange the equation to isolate \( x \):
\[ 9x + 45 - 30 = 10x \]
This simplifies to:
\[ 9x + 15 = 10x \]
Subtracting \( 9x \) from both sides:
\[ 15 = 10x - 9x \]
Thus:
\[ 15 = x \]

### Step 6: Calculate the number of white balls
Now that we have \( x = 15 \), we can find the number of white balls:
\[ \text{Number of white balls} = 3x + 10 = 3(15) + 10 = 45 + 10 = 55 \]

### Final Answer
The number of white balls is \( 55 \).

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