Set 7: Systems of Equations (Advanced)

Choice C is correct. 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: $\begin{cases} c + w = 50 \\ 2 c + 4 w = 140 \end{cases}$ Step 2: From first equation: $c = 50 - w$ Step 3: Substitute into second equation: 2(50 - w) + 4 w = 140$100- 2 w + 4 w = 1402w = 40w = 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$2(35) + 4(15) = 70 + 60 = 130 \neq 140$. Choice B is incorrect because$2(25) + 4(25) = 50 + 100 = 150 \neq 140$. Choice D is incorrect because$2(20) + 4(30) = 40 + 120 = 160 \neq 140$.