Question

What is the sum of two consecutive even integers divided by four is 189.5?

Answer 1

Let us denote the smaller even integer by $N$.
Then, the next even integer must be $N+2$.

To verify, set $N$ as any even number, say $174$.
Then, the next even integer must be 2 more than this number, i.e. $174+2=176$.

The sum of these two consecutive even integers can be expressed as:
                                    $N+(N+2)=2N+2$

We are told that this sum divided by four is 189.5, i.e.
                                     $(2N+2)\div4=189.5$

Multiplying both sides by 4 will reverse the division:
     $(2N+2)\div4\times4=189.5\times4$
     $(2N+2)\times1=758$

Subtracting 2 from each side will reverse the addition:
     $2N+2-2=758-2$
     $2N=756$

Dividing both sides by 2 will reverse the multiplication:
     $2N\div2=756\div2$
     $N=378$

Therefore, the two consecutive integers must be 378 and 380.

Check this:
     $(378+380)\div4=758\div4=189.5$