Find all pairs of consecutive even numbers which are greater than 8 and their sum is smaller then 27.

Explanation

To solve the problem of finding all pairs of consecutive even numbers greater than 8 whose sum is smaller than 27, we can follow these steps:

### Step 1: Define the Consecutive Even Numbers
Let the first even number be \( x \). The next consecutive even number will then be \( x + 2 \).

### Step 2: Set Up the Inequalities
According to the problem, we have two conditions:
1. The numbers must be greater than 8:
\[ x > 8 \]
2. Their sum must be smaller than 27:
\[ x + (x + 2) < 27 \]

### Step 3: Simplify the Sum Inequality
We can simplify the sum inequality:
\[ x + x + 2 < 27 \]
\[ 2x + 2 < 27 \]
Subtract 2 from both sides:
\[ 2x < 25 \]
Now, divide by 2:
\[ x < 12.5 \]

### Step 4: Combine the Inequalities
Now we have two inequalities to consider:
1. \( x > 8 \)
2. \( x < 12.5 \)

Combining these gives:
\[ 8 < x < 12.5 \]

### Step 5: Identify the Even Numbers
Since \( x \) must be an even number, the possible values for \( x \) that satisfy \( 8 < x < 12.5 \) are:
- \( x = 10 \)
- \( x = 12 \)

### Step 6: Find the Consecutive Even Numbers
Now we can find the pairs of consecutive even numbers:
1. If \( x = 10 \), then the consecutive even numbers are \( 10 \) and \( 12 \).
2. If \( x = 12 \), then the consecutive even numbers are \( 12 \) and \( 14 \).

### Conclusion
The pairs of consecutive even numbers greater than 8 and whose sum is smaller than 27 are:
- \( (10, 12) \)
- \( (12, 14) \)