Find out such pairs of consecutive even numbers in which both numbers are greater
than 5 and their sum is less than 26 .
Answers
Answered by
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).
Similar questions