Let the unknown numbers be x and y.
To solve this question, follow the steps below.
Step 01: Write a relation between the two numbers.
Given that "One number is 5 more than another number":
[tex]x=y+5[/tex]
Step 02: Write an equation for the sum of the numbers.
Given that the sum of the numbers is 13:
[tex]x+y=13[/tex]
Step 03: Substitute x from the first equation in the equation from step 02.
[tex]\begin{gathered} x+y=13 \\ y+5+y=13 \end{gathered}[/tex]
And solve the equation for y:
[tex]2y+5=13[/tex]
Subtracting 5 from both sides and then dividing the sides by 2:
[tex]\begin{gathered} 2y+5-5=13-5 \\ 2y=8 \\ \frac{2y}{2}=\frac{8}{2} \\ y=4 \end{gathered}[/tex]
Step 04: FInd x using the equation from step 01.
[tex]\begin{gathered} x=y+5 \\ x=4+5 \\ y=9 \end{gathered}[/tex]
Answer: The numbers are 4 and 9.
