Set 7: Systems of Equations (Advanced)

Choice C is correct. Choice C is the correct answer. Let $x$ = amount at 4% and $y$ = amount at 6%. Step 1: Set up the system: $\begin{cases} x + y = 5000 \\ 0.04 x + 0.06 y = 260 \end{cases}$ Step 2: From first equation: $x = 5000 - y$ Step 3: Substitute: 0.04(5000 - y) + 0.06 y = 260$200- 0.04 y + 0.06 y = 2600.02y = 60y = 3000$$ Solution: \3,000 was invested at 6% Verification: - $2,000 at 4%: $0.04(2000) = 80$ - $3,000 at 6%: $0.06(3000) = 180$ - Total interest: $80+ 180 = 260$ ✓ Strategic Tip: Investment problems: (principal × rate) = interest earned. Choice A is incorrect because $0.04(3000) + 0.06(2000) = 120 + 120 = 240 \neq 260$. Choice B is incorrect because $0.04(2500) + 0.06(2500) = 100 + 150 = 250 \neq 260$. Choice D is incorrect because $0.04(1500) + 0.06(3500) = 60 + 210 = 270 \neq 260$.