Verified Answer :

Let the 1st number represent x and the second number as y.  

\(x+(x+1)=223\)

\(2x+1=223\)

\(2x=222\)

\(2x/2=222/2\)  \(|Divide \ both \ sides \ by \ 2|\)

\(x=111\)  

\(y = 112\)

at most means less than ore equal to
consecutive integers are 1 apart
x and x+1
is less than or equal than 223

x+x+1≤223
2x+1≤223
mminus 1 both sides
2x≤222
divide 2
x≤111
larger is x+1
add 1 to both sides
x+1≤112

larger is 112 at most