Question

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

• A. 5
• B. 13
• C. 7
• D. 11
• E. 9

Hint:

Represent consecutive odd or even numbers algebraically to simplify the problem.

Answer 1

Answer: (E)

Step 1: Defining Variables:
Let the three consecutive odd numbers be \(n-2\), \(n\), and \(n+2\), where \(n\) is the middle number.

Step 2: Formulating the Equation:
Sum of the numbers = \((n-2) + n + (n+2) = 3n\).
The sum is 20 more than the first number \((n-2)\).
\[ 3n = (n-2) + 20 \]

Step 3: Solving for \(n\):
\[ 3n = n + 18 \]
\[ 3n - n = 18 \]
\[ 2n = 18 \]
\[ n = 9 \]

Step 4: Final Answer:
The middle number is 9.