Set 14: Systems of Equations (Intermediate)

Choice B is correct. Choice B is the correct answer. Let $p$ = pounds of peanuts. Step 1: Set up the equation: $\frac{12(10) + 6 p}{10 + p} = 9$ The numerator is total value, denominator is total weight. Step 2: Multiply both sides by $(10 + p)$: $$$120+ 6 p = 9(10 + p)$120+ 6 p = 90 + 9 p$120- 90 = 9 p - 6 p30= 3 p$p = 10 Solution: 10 pounds of peanuts Verification: - Total value: $12(10) + 6(10) = 120 + 60 = 180$ - Total weight: $10+ 10 = 20$ - Price per pound: $\frac{180}{20} = 9$ ✓ Strategic Tip: Mixture problems: (sum of values) ÷ (sum of quantities) = average price. Choice A is incorrect because $\frac{120 + 48}{18} = \frac{168}{18} \approx 9.33 \neq 9$. Choice C is incorrect because $\frac{120 + 72}{22} = \frac{192}{22} \approx 8.73 \neq 9$. Choice D is incorrect because $\frac{120 + 90}{25} = \frac{210}{25} = 8.4 \neq 9$.