Let us denote the smaller even integer by [tex]N[/tex].
Then, the next even integer must be [tex]N+2[/tex].
To verify, set [tex]N[/tex] as any even number, say [tex]174[/tex].
Then, the next even integer must be 2 more than this number, i.e. [tex]174+2=176[/tex].
The sum of these two consecutive even integers can be expressed as:
[tex]N+(N+2)=2N+2[/tex]
We are told that this sum divided by four is 189.5, i.e.
[tex](2N+2)\div4=189.5[/tex]
Multiplying both sides by 4 will reverse the division:
[tex](2N+2)\div4\times4=189.5\times4[/tex]
[tex](2N+2)\times1=758[/tex]
Subtracting 2 from each side will reverse the addition:
[tex]2N+2-2=758-2[/tex]
[tex]2N=756[/tex]
Dividing both sides by 2 will reverse the multiplication:
[tex]2N\div2=756\div2[/tex]
[tex]N=378[/tex]
Therefore, the two consecutive integers must be 378 and 380.
Check this:
[tex](378+380)\div4=758\div4=189.5[/tex]
