document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1067268>Question 1067268</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose you have 16 coins that equal at least $2.20. Some coins are quarters and some are nickels. What is the greatest amount of nickels you can have? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #682476 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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/cgi-bin/show-face.mpl?user=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=682476\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let n = number of nickels, q = number of quarters.\r<BR>\n" );
document.write( "\n" );
document.write( "Then we have  n+q =16  and  .05n+.25q >= 2.20\r<BR>\n" );
document.write( "\n" );
document.write( "Notice that we have two other constraints.   0<=n=<16 and 0<=q<=16\r<BR>\n" );
document.write( "\n" );
document.write( "So  the solution that gives us exactly 16 coins and exactly 2.20 would be set by\r<BR>\n" );
document.write( "\n" );
document.write( "n+q=16 and .05n+.25q=2.20\r<BR>\n" );
document.write( "\n" );
document.write( "q=16-n by solving the 1st equation for q.\r<BR>\n" );
document.write( "\n" );
document.write( ".05n + .25(16-n) = 2.20\r<BR>\n" );
document.write( "\n" );
document.write( ".05n + 4 - .25n = 2.20\r<BR>\n" );
document.write( "\n" );
document.write( ".2n = 1.80\r<BR>\n" );
document.write( "\n" );
document.write( "n = 9  (so q = 7)\r<BR>\n" );
document.write( "\n" );
document.write( "So n is at least 9.\r<BR>\n" );
document.write( "\n" );
document.write( "Now, the question is what is the greatest?\r<BR>\n" );
document.write( "\n" );
document.write( "We can logically say that for every nickel I add, I have to subtract a quarter (meaning the net amount of money is decreased by 20 cents).\r<BR>\n" );
document.write( "\n" );
document.write( "So for instance if n = 10, then q = 6, so we have .5 + 1.50 = 2.00 (which isn't at least 2.20). \r<BR>\n" );
document.write( "\n" );
document.write( "Now we can have n=8 and we will go to 2.40, but that's not the \"maximum\" number of nickels.\r<BR>\n" );
document.write( "\n" );
document.write( "So, the maximum number of nickels is 9.\r<BR>\n" );
document.write( "\n" );
document.write( "I'll attempt to graph what is going on.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28500%2C500%2C0%2C16%2C0%2C16%2Cy=16-x%2Cy%3E=8.8-.2x%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C0%2C16%2C0%2C16%2Cy=16-x%2Cy%3E=8.8-.2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "This is using q = 16-n<BR>\n" );
document.write( "and  q >= 8.8-.2n<BR>\n" );
document.write( "Notice that the intersection of the graphs for (n,q) is (9,7) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );