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