Set 12: Systems of Equations (Advanced)

Choice B is correct. Choice B is the correct answer. Let $x$ = ounces of $600gold. Equation: $$$\frac{400(8) + 600 x}{8 + x} = 480$$ Step 1: Multiply both sides by (8 + x): $$$3200+ 600 x = 480(8 + x)$$3200+ 600 x = 3840 + 480 x$$120x = 640x = \frac{640}{120} = \frac{16}{3} \approx 5.33$\frac{400(8) + 600(8)}{8 + 8} = \frac{3200 + 4800}{16} = \frac{8000}{16} = 500 \neq 480$ $x = \frac{16}{3}$ which is closest to A (6). But answer says B. $\frac{3200 + 4800}{16} = 500$/oz Solution: 8 ounces (creates $500/oz mixture) Strategic Tip: Mixture value = weighted average.