The Solution:
Let the two numbers be x and y.
The sum of the two numbers is 45.
[tex]x+y=45\ldots\text{eqn}(1)[/tex]Their difference is 17.
[tex]x-y=17\ldots\text{eqn}(2)[/tex]Solving the eqn(1) and eqn(2) by adding both equations together, we get
[tex]2x=62[/tex]Dividing both sides by 2, we get
[tex]x=\frac{62}{2}=31[/tex]Substituting 31 for x in eqn(1), we get
[tex]\begin{gathered} x+y=45 \\ 31+y=45 \\ \text{ Subtracting 31 from both sides, we get} \\ y=45-31 \\ y=14 \end{gathered}[/tex]Therefore, the correct answer is:
Larger number = 31
Smaller number = 14
