SAT Math · Linear functions · medium

Company A charges a flat fee of 60 plus 2 per unit produced. Company B charges a flat fee of 20 plus 4 per unit produced. At how many…

Company A charges a flat fee of $60 plus $2 per unit produced. Company B charges a flat fee of $20 plus $4 per unit produced. At how many units do the two companies charge the same total amount?

Answer and explanation

Answer: D: 20

Write each company's total cost for nn units: Company A is 60+2n60 + 2n and Company B is 20+4n20 + 4n. The costs match when 60+2n=20+4n60 + 2n = 20 + 4n. Subtract 2n2n and 20 from both sides: 40=2n40 = 2n, so n=20n = 20, choice D. Check: A charges 60+40=$10060 + 40 = \$100 and B charges 20+80=$10020 + 80 = \$100. Choice A (15) and choice C (10) give different totals. Choice B (40) is the difference in flat fees, which is a value on the way to the answer, not the final step. Divide by the difference in per-unit rates.

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