Find the missing number if the average of all the eight number is 474.
533,128,429,225_____,305,601,804

Options

A. 767
B. 781
C. 776
D. 758

Explanation

To find the missing number in the given set of numbers where the average is 474, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Average Formula**:
The average of a set of numbers is calculated by dividing the sum of all the numbers by the total count of numbers. In this case, we have 8 numbers.

\[ \text{Average} = \frac{\text{Sum of all numbers}}{\text{Total count of numbers}} \]

2. **Set Up the Equation**:
Given that the average is 474, we can set up the equation:

\[ 474 = \frac{533 + 128 + 429 + 225 + x + 305 + 601 + 804}{8} \]

Here, \( x \) is the missing number.

3. **Multiply Both Sides by 8**:
To eliminate the fraction, multiply both sides of the equation by 8:

\[ 474 \times 8 = 533 + 128 + 429 + 225 + x + 305 + 601 + 804 \]

4. **Calculate the Left Side**:
Calculate \( 474 \times 8 \):

\[ 474 \times 8 = 3792 \]

5. **Calculate the Sum of Known Numbers**:
Now, add the known numbers together:

\[ 533 + 128 + 429 + 225 + 305 + 601 + 804 \]

Let's break this down step by step:
- \( 533 + 128 = 661 \)
- \( 661 + 429 = 1090 \)
- \( 1090 + 225 = 1315 \)
- \( 1315 + 305 = 1620 \)
- \( 1620 + 601 = 2221 \)
- \( 2221 + 804 = 3025 \)

So, the sum of the known numbers is 3025.

6. **Set Up the Final Equation**:
Now, we can set up the equation to find \( x \):

\[ 3792 = 3025 + x \]

7. **Solve for \( x \)**:
To find \( x \), subtract 3025 from both sides:

\[ x = 3792 - 3025 \]

Now calculate:

\[ x = 767 \]

### Final Answer:
The missing number is **767**.