Let's say that the numbers are x and y. So, we know that....
x+y=186
y-x=22
Now we can use the substitution method to find the numbers. y-x=22 turns into y=22+x. And now we can substitute to the second equation into the first equation.
x+22+x=186
2x=164
x=82
y=22+82
y=104
Our numbers are 82 and 104 and the larger integer is 104, so that's the answer.
