ACT Math · Linear equations and inequalities

A company spends 2,000 to set up production, plus 15 per unit produced. Each unit sells for $35. How many units must be sold to break even?

A company spends $2,000 to set up production, plus $15 per unit produced. Each unit sells for $35. How many units must be sold to break even?

Answer and explanation

Answer: C: 100

Revenue equals cost at break-even. Revenue is 35x35x, and total cost is 2000+15x2000+15x. Set them equal: 35x=2000+15x35x=2000+15x, so 20x=200020x=2000 and x=100x=100 units, choice C. Check: revenue is $3,500, and cost is 2000+1500=35002000+1500=3500. Each unit contributes $20 toward the setup cost, because 35−15=2035-15=20. Choice B (5757) divides the setup cost by the selling price, 200035\frac{2000}{35}, ignoring the per-unit cost. Choice D (133133) divides by $15 instead of $20. Choice A (4040) is 200050\frac{2000}{50}, which uses the sum of the costs and price incorrectly.

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