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Analyzing Copier and Printer Charges

Compare charges for Acme Copiers and Best Printers based on monthly fee and per-copy cost. Analyze when each is cheaper depending on the number of copies.

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Analyzing Copier and Printer Charges

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  1. Objective- To use tables to compare linear expressions. Acme Copiers charges $250 per month and one cent per copy. Best Printers charges $70 per month and three cents per copy. When is Acme cheaper? Let n = the number of copies Let C = the total charge Acme Best C = 250 + .01n C = 70 + .03n

  2. Let n = number copies Let C = total charge Acme Best C = 250 + .01n C = 70 + .03n n Acme Charge Best Charge 250 + .01( 0 ) = 250 70 + .03( 0 ) = 70 0 2,000 250 + .01(2,000) = 270 70 + .03(2,000) = 130 4,000 250 + .01(4,000) = 290 70 + .03(4,000) = 190 6,000 250 + .01(6,000) = 310 70 + .03(6,000) = 250 8,000 330 310 10,000 350 370 12,000 370 430 14,000 390 490 410 550 16,000 18,000 430 610

  3. Let n = number copies Let C = total charge Acme Best C = 250 + .01n C = 70 + .03n n Acme Charge Best Charge 250 + .01( 0 ) = 250 70 + .03( 0 ) = 70 0 2,000 250 + .01(2,000) = 270 70 + .03(2,000) = 130 4,000 250 + .01(4,000) = 290 70 + .03(4,000) = 190 6,000 250 + .01(6,000) = 310 70 + .03(6,000) = 250 8,000 330 310 10,000 350 370 Best is cheaper at 8,000 copies, but Acme is cheaper at 10,000 copies.

  4. Let n = number copies Let C = total charge Acme Best C = 250 + .01n C = 70 + .03n n Acme Charge Best Charge 8,000 250 + .01(8,000) = 330 70 + .03(8,000) = 310 8,500 250 + .01(8,500) = 335 70 + .03(8,500) = 325 9,000 250 + .01(9,000) = 340 70 + .03(9,000) = 340 9,500 250 + .01(9,500) = 345 70 + .03(9,500) = 355 10,000 350 370 Acme is cheaper at more than 9,000 copies.

  5. A Better Way ! Let n = number copies Let C = total charge Acme Best C = 250 + .01n C = 70 + .03n When do they cost the same? 250 + .01n = 70 + .03n - .01n - .01n 250 = 70 + .02n They cost the same at 9000 copies. 180 = .02n .02 .02 9000 = n

  6. A Better Way ! Let n = number copies Let C = total charge Acme Best C = 250 + .01n C = 70 + .03n When does Acme cost less? 250 + .01n < 70 + .03n - .01n - .01n 250 < 70 + .02n 180 < .02n .02 .02 n > 9000 copies 9000 < n

  7. The Willoughby family wants to rent a convertible for a day. “Let it Ride” company charges $32 a day and 25 cents a mile. For the same kind of car, “Rollin’ Down the Highway” charges $29 a day and 30 cents a mile. For what number of miles will the two rental costs be the same? Miles “Let it Ride” “Rollin’ Down the Highway” • 38.25 36.50 • 44.50 44.00 • 75 50.75 51.50

  8. Miles “Let it Ride” “Rollin’ Down the Highway” 32.00 35.00 38.00 41.00 44.00 47.00 50.00 53.00 10 20 30 40 50 60 70 80 34.50 37.00 39.50 42.00 44.50 47.00 49.50 52.00 The two companies cost the same for 60 miles. “Let it Ride” cost less after 60 miles and “Rollin’ Down the Highway cost less under 60 miles.

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