Find all pairs of consecutive odd natural numbers, both of which are larger than 10 , such that their sum is less than 40 .

Step 1: Define the numbers

Let the first odd natural number be $x$. Since the numbers are consecutive odd natural numbers, the next odd natural number will be $x+2$.

Step 2: Set up inequalities based on conditions

We are given two conditions: both numbers must be larger than 10, which means $x > 10$. Also, their sum must be less than 40, so $x + (x+2) < 40$.

Step 3: Solve the sum inequality

Simplify the sum inequality: $2x + 2 < 40$. Subtract 2 from both sides to get $2x < 38$. Then, divide by 2 to find $x < 19$.

Step 4: Combine conditions for x

Combining the conditions $x > 10$ and $x < 19$, we find that $x$ must be an odd natural number between 10 and 19.

Step 5: Identify possible values for x and pairs

The odd natural numbers greater than 10 and less than 19 are 11, 13, 15, and 17. For each of these values of $x$, we find the corresponding consecutive odd number $x+2$ to form the pairs.

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