Set 6: Systems of Equations (Advanced)

Choice C is correct. Choice C is the correct answer. Let $m$ = motorcycles and $c$ = cars. System: $\begin{cases} m + c = 35 \\ 2 m + 4 c = 110 \end{cases}$ Step 1: From first equation: $m = 35 - c$ Step 2: Substitute: 2(35 - c) + 4 c = 110$70- 2 c + 4 c = 1102c = 40c = 20$$ Step 3: Find m: $$m = 35 - 20 = 15$$ - 15 motorcycles + 20 cars = 35 vehicles ✓ - Wheels: 2(15) + 4(20) = 30 + 80 = 110$✓ - 10 motorcycles + 25 cars = 35 vehicles ✓ - Wheels:$2(10) + 4(25) = 20 + 100 = 120 \neq 110$Strategic Tip: Count vehicles for one equation, wheels for another. Choice A is incorrect because$2(15) + 4(20) = 30 + 80 = 110 \neq 120$. Choice B is incorrect because$2(20) + 4(15) = 40 + 60 = 100 \neq 120$. Choice D is incorrect because$2(25) + 4(10) = 50 + 40 = 90 \neq 120$.