Set 12: Systems of Equations (Intermediate)

Choice D is correct. Choice D is the correct answer. Let $s$ = amount in stocks and $b$ = amount in bonds. System: $\begin{cases} s + b = 8000 \\ 0.08 s + 0.05 b = 550 \end{cases}$ Step 1: From first: $b = 8000 - s$ Step 2: Substitute: $$$0.08s + 0.05(8000 - s) = 550$0.08s + 400 - 0.05 s = 550$0.03s = 150s = 5000$$ Solution: \5,000 in stocks (and $3,000 in bonds) Verification: $0.08(5000) + 0.05(3000) = 400 + 150 = 550$ ✓ Strategic Tip: Investment interest = principal × rate. Choice A is incorrect because $0.08(3000) + 0.05(5000) = 240 + 250 = 490 \neq 550$. Choice B is incorrect because $0.08(3500) + 0.05(4500) = 280 + 225 = 505 \neq 550$. Choice C is incorrect because $0.08(4000) + 0.05(4000) = 320 + 200 = 520 \neq 550$.