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Question
Find all pairs of consecutive odd natural number, both of which are larger than 10, such that their sum is less than 40.
Solution
Let x be the smaller of the two odd natural numbers. Then, the other odd natural number will be x + 2.
Therefore, as per the given conditions:
\[x > 10 \text{ and } x + x + 2 < 40\]
\[ \Rightarrow x > 10 \text{ and } 2x + 2 < 40\]
\[ \Rightarrow x > 10 \text{ and } x < 19\]
\[ \Rightarrow 10 < x < 19\]
\[ \therefore x \in \left\{ 11, 13, 15, 17 \right\}\]
\[\text{ Hence, the pairs are } (11, 13), (13, 15), (15, 17), (17, 19) .\]
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