Question 657224
Let x = the certain number, and x+1 = the next consecutive number.

Then we have:

{{{x/2 + (x+1)/3 = 22}}}

{{{(3/3) * (x/2) + (2/2)*((x+1)/3) = 22}}}

{{{3x/6 + (2x+2)/6 = 22}}}

Multiplying both sides by 6:

{{{3x + 2x + 2 = 132}}}

{{{5x = 130}}}

{{{x = 26}}}

Confirming:

{{{(26/2) + (27/3) = 13 + 9 = 22}}}