Explanation
This is a word problem leading to a simultaneous equation
Let the small number be x
Let the large number be y
so we will have
[tex]\begin{gathered} x+y=55 \\ y=x+23 \end{gathered}[/tex][tex]\begin{gathered} solving\text{ for x and y} \\ \\ \mathrm{Substitute\:}y=x+23 \\ x+x+23=55 \\ \\ 2x=55-23 \\ 2x=32 \\ x=16 \\ \\ y=55-16=39 \\ y=39 \end{gathered}[/tex]Therefore
The larger number is 39
Smaller number is 16
