The average of 5 consecutive odd numbers is 75. By adding which number, will the average become 76?

Options

A. a)81
B. b)79
C. c)76
D. d)77

Answer

To solve the problem step by step, we need to find the number that, when added to the average of five consecutive odd numbers (which is 75), will result in a new average of 76.

### Step 1: Understand the average of the numbers
The average of 5 consecutive odd numbers is given as 75. This means that the sum of these 5 numbers can be calculated as:
\[ \text{Sum} = \text{Average} \times \text{Number of terms} = 75 \times 5 = 375 \]

**Hint:** Remember that the average is the sum of the numbers divided by the number of terms.

### Step 2: Identify the new average
We want to find out what number we need to add to this sum to make the average of the new set of numbers equal to 76. If we add one more number (let's call it \( x \)), the total number of terms will become 6.

**Hint:** When you add a number to a set, the total number of terms increases by one.

### Step 3: Set up the equation for the new average
The new average after adding the number \( x \) can be expressed as:
\[ \text{New Average} = \frac{\text{Sum of original numbers} + x}{\text{Total number of terms}} \]
Substituting the known values:
\[ 76 = \frac{375 + x}{6} \]

**Hint:** The new average is calculated by dividing the new total sum by the new total number of terms.

### Step 4: Solve for \( x \)
To find \( x \), we can multiply both sides of the equation by 6:
\[ 76 \times 6 = 375 + x \]
Calculating the left side:
\[ 456 = 375 + x \]
Now, isolate \( x \) by subtracting 375 from both sides:
\[ x = 456 - 375 = 81 \]

**Hint:** Isolating the variable helps in finding its value directly.

### Conclusion
The number that needs to be added to the sum of the 5 consecutive odd numbers to make the average 76 is \( 81 \).

**Final Answer:** 81