Question 493824
Let x be the first integer.

Then x + (x+1) + (x+2) are three consecutive integers.

We know that the sum of the second (x+1) and the third (x+2) is (x+33)/2

So  {{{(x+1) + (x+2) = x/2 + 33}}}

Combine and simplify

{{{ 2x +3 = x/2 + 33}}}
Subtract 33 on both sides.
{{{ 2x-30 = x/2}}}
Multiply by 2 on both sides
{{{4x -60 = x}}}
Combine like terms.
{{{-60 = -3x}}}
Divide by -3
{{{x = 20}}}

So the consecutive integers are 20,21,22.