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
Let n = number copies Let C = total charge Acme Best C = 250 + .01n C = 70 + .03n n Acme Charge Best Charge
0 2,000 4,000 6,000 8,000
10,000 12,000
250 + .01( 0 ) = 250 70 + .03( 0 ) = 70 250 + .01(2,000) = 70 + .03(2,000) = 130 270 + .01(4,000) = 290 70 + .03(4,000) = 190 250 250 + .01(6,000) = 310 70 + .03(6,000) = 250 330 310
350 370 370 430
14,000
16,000 18,000
390 410
430
490 550
610
Let n = number copies Let C = total charge Acme Best C = 250 + .01n C = 70 + .03n n Acme Charge Best Charge
0 2,000 4,000 6,000 8,000
10,000
250 + .01( 0 ) = 250 70 + .03( 0 ) = 70 250 + .01(2,000) = 70 + .03(2,000) = 130 270 + .01(4,000) = 290 70 + .03(4,000) = 190 250 250 + .01(6,000) = 310 70 + .03(6,000) = 250 330 310
350 370
Best is cheaper at 8,000 copies, but Acme is cheaper at 10,000 copies.
Let n = number copies Let C = total charge Acme Best C = 250 + .01n C = 70 + .03n n Acme Charge Best Charge
8,000 8,500 9,000
250 + .01(8,000) = 330 250 + .01(8,500) = 335 + .01(9,000) = 340 250 250 + .01(9,500) = 345 350
70 + .03(8,000) = 310
70 + .03(8,500) = 325 70 + .03(9,000) = 340
9,500 10,000
70 + .03(9,500) = 355
370
Acme is cheaper at 9,000 copies or more
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 180 = .02n same at .02 .02 9000 copies. 9000 = n