Choice C is the correct answer. Let $x$ be the larger number and $y$ be the smaller number.

System: $\begin{cases} x + y = 24 \\ x - y = 8 \end{cases}$

Step 1: Add the equations to eliminate $y$: $2x = 32$$x = 16$

Step 2: Find $y$ using $x + y = 24$: $16 + y = 24$$y = 8$

Solution: The larger number is 16.

Verification: $16 + 8 = 24$ ✓ and $16 - 8 = 8$ ✓

💡 Strategic Tip: Sum and difference problems are perfect for elimination method.

Choice A is incorrect because$14 + 10 = 24$ ✓, but $14 - 10 = 4 \ eq 8$.

Choice B is incorrect because$18 + 6 = 24$ ✓, but $18 - 6 = 12 \ eq 8$.

Choice D is incorrect because this is the smaller number, not the larger one.