Set 10: Systems of Equations (Advanced)

Choice B is correct. Choice B is the correct answer. Break-even occurs when Cost = Revenue. Analysis: Let $x$ = number of widgets - Total Cost: $C = 500 + 3 x$ (fixed + variable) - Total Revenue: $R = 8 x$ Step 1: Set Cost = Revenue: $$$500+ 3 x = 8 x500= 5 x$x = 100 Solution: 100 widgets Verification: - Cost: $500+ 3(100) = 800$ - Revenue: $8(100) = 800$ ✓ Strategic Tip: Break-even analysis: find where revenue equals total cost (fixed + variable). Choice A is incorrect because at 80: Cost = $740, Revenue = 640 dollars (loss). Choice C is incorrect because at 120: Cost =$860, Revenue = 960 dollars (profit, past break-even). Choice D is incorrect because at 150: Cost = $950, Revenue = 1200 dollars (profit, past break-even).