Set 8: Systems of Equations

Choice B is correct. Choice B is the correct answer. Let $x$ = amount at 5% and $y$ = amount at 8%. System: $\begin{cases} x + y = 15000 \\ 0.05 x + 0.08 y = 990 \end{cases}$ Step 1: From first: $y = 15000 - x$ Step 2: Substitute: $$$0.05x + 0.08(15000 - x) = 9900.05x + 1200 - 0.08 x = 990$-0.03 x = -210x = 7000 Solution: $7,000 at 5% (and $8,000 at 8%) Verification: $0.05(7000) + 0.08(8000) = 350 + 640 = 990$ ✓ Strategic Tip: Investment problems: Principal × Rate = Interest. Other choices fail verification.