Set 1: Systems of Equations (Intermediate)

Choice B is correct. Choice B is the correct answer. Let $x$ = liters of 20% solution and $y$ = liters of 50% solution. Step 1: Set up the system: $\begin{cases} x + y = 30 \\ 0.20 x + 0.50 y = 0.35(30) \end{cases}$ Step 2: Simplify second equation: $0.20x + 0.50 y = 10.5$ Multiply by 10: $2x + 5 y = 105$ Step 3: From first equation: $y = 30 - x$ Substitute: $$$2x + 5(30 - x) = 1052x + 150 - 5 x = 105$-3 x = -45x = 15 Solution: 15 liters of 20% solution (and 15 liters of 50% solution) Verification: $15+ 15 = 30$ ✓ and $0.20(15) + 0.50(15) = 3 + 7.5 = 10.5 = 0.35(30)$ ✓ Strategic Tip: In mixture problems, (concentration × volume) gives the amount of pure substance. Choice A is incorrect because $0.20(10) + 0.50(20) = 2 + 10 = 12 \neq 10.5$. Choice C is incorrect because $0.20(18) + 0.50(12) = 3.6 + 6 = 9.6 \neq 10.5$. Choice D is incorrect because $0.20(12) + 0.50(18) = 2.4 + 9 = 11.4 \neq 10.5$.