Choice C is the correct answer. Let $x$ be the larger number and $y$ be the smaller number. We can set up a system of equations.

System: $\begin{cases} x + y = 15 \\ x - y = 5 \end{cases}$

Step 1: Add the equations to eliminate $y$: $2x = 20$$x = 10$

Step 2: Substitute $x = 10$ into $x + y = 15$: $10 + y = 15$$y = 5$

Solution: The numbers are 10 and 5.

Verification: $10 + 5 = 15$ ✓ and $10 - 5 = 5$ ✓

💡 Strategic Tip: Word problems involving "sum" and "difference" naturally lead to systems with opposites.

Choice A is incorrect because$8 + 7 = 15$ ✓, but $8 - 7 = 1 \ eq 5$.

Choice B is incorrect because$12 - 3 = 9 \ eq 5$.

Choice D is incorrect because$9 + 6 = 15$ ✓, but $9 - 6 = 3 \ eq 5$.