Choice C is the correct answer. Let $c$ = chickens and $w$ = cows.

Note: Chickens have 2 legs, cows have 4 legs, both have 1 head.

Step 1: Set up the system: $\begin{cases} c + w = 50 \\ 2c + 4w = 140 \end{cases}$

Step 2: From first equation: $c = 50 - w$

Step 3: Substitute into second equation: $2(50 - w) + 4w = 140$$100 - 2w + 4w = 140$$2w = 40$$w = 20$

Step 4: Find $c$: $c = 50 - 20 = 30$

Solution: 30 chickens (and 20 cows)

Verification: $30 + 20 = 50$ heads ✓ and $2(30) + 4(20) = 60 + 80 = 140$ legs ✓

💡 Strategic Tip: In "heads and legs" problems, count heads for one equation and legs for another.

Choice A is incorrect because $2(35) + 4(15) = 70 + 60 = 130 \ eq 140$.

Choice B is incorrect because $2(25) + 4(25) = 50 + 100 = 150 \ eq 140$.

Choice D is incorrect because $2(20) + 4(30) = 40 + 120 = 160 \ eq 140$.