document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=84336>Question 84336</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534465390/algebrahomeworkh>finite mathmatics</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Please help with solution and how obtained for this question.\r<BR>\n" );
document.write( "\n" );
document.write( "One printing shop charges $5 plus $0.02 per page and a second shop charges $7 plus $0.015 per page. If __________ pages are printed, the total cost is less for the first printing shop.\r<BR>\n" );
document.write( "\n" );
document.write( "A. less than 1500<BR>\n" );
document.write( "B. less than 2100<BR>\n" );
document.write( "C. less than 400<BR>\n" );
document.write( "D. less than 900 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #60750 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=60750\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Begin by writing the equations for the Cost (C) of each printer. The general form of these<BR>\n" );
document.write( "equations is based on multiplying the cost per page times the number of pages and adding<BR>\n" );
document.write( "to that the fixed cost that you pay regardless of the number of pages.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "For the first printer, the equation for the Cost (C) and the number of pages (P) is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "C = (0.02*P) + 5<BR>\n" );
document.write( ".<BR>\n" );
document.write( "For the second printer, the equation for the Cost (C) is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "C = (0.015*P) + 7<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The first printer is cheaper for a while. You can tell that because if you have 1 page<BR>\n" );
document.write( "printed, the cost at the first printer is $5.02 and the cost at the second printer is<BR>\n" );
document.write( "$7.015. However, as you increase the number of pages, the difference in the Cost between<BR>\n" );
document.write( "the two printers gets smaller and smaller until at some number of pages the Cost of the <BR>\n" );
document.write( "two printers is the same.  After that number of pages, the Cost for printing more pages<BR>\n" );
document.write( "will be less at Printer 2.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "You can find the point at which the number of pages make the Cost equal at the two printers.<BR>\n" );
document.write( "Do this by solving the two Cost equations simultaneously.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The two equations are:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "C = (0.02*P) +  5 <BR>\n" );
document.write( "C = (0.015*P) + 7<BR>\n" );
document.write( ".<BR>\n" );
document.write( "We are trying to find the number of pages (P) that will make the Costs equal. Notice that<BR>\n" );
document.write( "if C is the same in both equations then the right side of both equations must be equal<BR>\n" );
document.write( "also. So we can say:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(0.02*P) + 5 = (0.015*P) + 7<BR>\n" );
document.write( ".<BR>\n" );
document.write( "To solve this requires collecting the terms that have P on one side of the equation<BR>\n" );
document.write( "and the numbers on the other side.  You can start by subtracting (0.015*P) from both sides<BR>\n" );
document.write( "of the equation. This makes the equation become:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(0.02*P) - (0.015*P) + 5 = + 7<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Next subtract 5 from both sides. This results in:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(0.02*P) - (0.015*P) = + 2<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Then subtract the two terms on the left side to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "0.005*P = 2<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Finally, solve for P by dividing both sides by 0.005, the multiplier of P. The solution<BR>\n" );
document.write( "for P is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "P = 2/0.005 = 400<BR>\n" );
document.write( ".<BR>\n" );
document.write( "So if you have 400 pages to print, the Cost should be equal at the two printers. Check this<BR>\n" );
document.write( "out. <BR>\n" );
document.write( ".<BR>\n" );
document.write( "The Cost at the first printer would be $5.00 plus 2 cents a page for the 400 pages<BR>\n" );
document.write( "which is 800 cents or $8.00. So the total cost is $5 + $8 = $13.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The Cost at the second printer would be $7.00 plus 1.5 cents a page for 400 pages <BR>\n" );
document.write( "which is 600 cents or $6.00. That makes the the total Cost $7 + $6 = $13.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Since the Cost is $13 at each printer for 400 pages, you can draw the following conclusion:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "For less than 400 pages, it will be cheaper to use the first printer.  At 400 pages it<BR>\n" );
document.write( "doesn't matter which printer you use, the Cost will be the same.  For any number of pages<BR>\n" );
document.write( "greater than 400, you will save money by using the second printer.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Answer C is the correct answer.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );