Set 9: Systems of Equations (Advanced)

Choice A is correct. Choice A is the correct answer. Let $c$ = chocolate bars and $l$ = lollipops. System: $\begin{cases} c + l = 20 \\ 2 c + 0.5 l = 25 \end{cases}$ Step 1: From first equation: $l = 20 - c$ Step 2: Substitute: $$$2c + 0.5(20 - c) = 25$2c + 10 - 0.5 c = 25$1.5c = 15c = 10$$ Solution: 10 chocolate bars (and 10 lollipops) Verification: $$10+ 10 = 20$$ ✓ and 2(10) + 0.5(10) = 20 + 5 = 25✓ Strategic Tip: Convert decimals to fractions if it helps: $$0.5= \frac{1}{2}$$. Choice B is incorrect because2(12) + 0.5(8) = 24 + 4 = 28 \neq 25$. Choice C is incorrect because$2(15) + 0.5(5) = 30 + 2.5 = 32.5 \neq 25$. Choice D is incorrect because$2(8) + 0.5(12) = 16 + 6 = 22 \neq 25$.