Question

Find out such pairs of consecutive even numbers in which both numbers are greater
than 5 and their sum is less than 26 .​

Answer 1

Answer:

Let x be smaller of two consecutive even positive integers. Then the other integer is x+2.

Both integers are larger than 5.

\therefore \, \, \, x> 5

Sum of both integers is less than 23.

\therefore \, \, \, x+(x+2)< 23

\Rightarrow \, \, \, (2x+2)< 23

\Rightarrow \, \, \, 2x< 23-2

\Rightarrow \, \, \, 2x< 21

\Rightarrow \, \, \, x< \frac{21}{2}

\Rightarrow \, \, \, x< 10.5

We conclude \, \, \, \, x< 10.5 and \, \, \, x> 5 and x is even integer number.

x can be 6,8,10.

The pairs of consecutive even positive integers are (6,8),(8,10),(10,12).