The sum of three consecutive odd numbers is 20 more than the first of these numbers. What is the middle number ?

Options

A. 7
B. 9
C. 11
D. Data inadequate

Answer

To solve the problem of finding the middle number of three consecutive odd numbers whose sum is 20 more than the first number, we can follow these steps:

### Step 1: Define the Variables
Let the first odd number be \( x \). Since we are dealing with consecutive odd numbers, the second odd number will be \( x + 2 \) and the third odd number will be \( x + 4 \).

### Step 2: Write the Equation
According to the problem, the sum of these three consecutive odd numbers is 20 more than the first number. We can express this mathematically:
\[ x + (x + 2) + (x + 4) = x + 20 \]

### Step 3: Simplify the Left Side
Now, simplify the left side of the equation:
\[ x + x + 2 + x + 4 = 3x + 6 \]
So, the equation now looks like:
\[ 3x + 6 = x + 20 \]

### Step 4: Rearrange the Equation
Next, we will rearrange the equation to isolate \( x \):
\[ 3x + 6 - x = 20 \]
This simplifies to:
\[ 2x + 6 = 20 \]

### Step 5: Solve for \( x \)
Now, subtract 6 from both sides:
\[ 2x = 20 - 6 \]
\[ 2x = 14 \]
Now, divide both sides by 2:
\[ x = 7 \]

### Step 6: Find the Middle Number
Now that we have the first number \( x = 7 \), we can find the middle number:
\[ \text{Middle number} = x + 2 = 7 + 2 = 9 \]

### Conclusion
Thus, the middle number is **9**.

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