Understanding Consecutive Odd Numbers

The problem asks us to find the larger of two consecutive odd numbers that add up to 24. Consecutive odd numbers are odd numbers that follow each other in sequence, like 3 and 5, or 11 and 13. The difference between any two consecutive odd numbers is always 2.

Setting up the Equation

Let's represent the two consecutive odd numbers using algebra:

• Let the smaller odd number be represented by the variable $x$.
• Since the numbers are consecutive odd numbers, the next odd number will be \(x + 2\).

The problem states that the sum of these two numbers is 24. We can write this as an equation:

\(x + (x + 2) = 24\)

Solving the Equation

Now, we need to solve this equation to find the value of $x$:

1. Combine the like terms: The equation simplifies to \(2x + 2 = 24\).
2. Isolate the term with $x$: Subtract 2 from both sides of the equation. \(2x + 2 - 2 = 24 - 2\) \(2x = 22\)
3. Solve for $x$: Divide both sides by 2. \(\frac{2x}{2} = \frac{22}{2}\) \(x = 11\)

So, the smaller odd number is 11.

Finding the Larger Number

The question asks for the larger number. We know the smaller number is \(x = 11\). The larger consecutive odd number is \(x + 2\).

Larger number = \(11 + 2 = 13\).

Verification

Let's check if our numbers satisfy the condition:

• The two numbers are 11 and 13.
• Are they consecutive odd numbers? Yes.
• Is their sum 24? \(11 + 13 = 24\). Yes.

Therefore, the larger number is indeed 13.