document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=182833>Question 182833</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Christina makes a $9.25 purchase at a bookstore in Reno with a $20 bill. The store has no bills and gives her the change in quarters and fifty cent pieces. There are 30 coins in all. How many of each kind are there? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #137322 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=137322\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The amount of change was <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 20.00 - 9.25 = 11.75\">.  Easier to use whole numbers so change that to 1175 cents.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let <i>q</i> be the number of quarters and <i>f</i> be the number of half-dollars.  Since there were 30 coins:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math q + f = 30 \ \ \Rightarrow\ \ f = 30 - q\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The value of the quarters is 25 cents times the number of quarters, or <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 25q\">.  Likewise, the value of the half-dollars is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 50f\">.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The value of the quarters plus the value of the half-dollars must total the amount of change, or 1175 cents.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math 25q + 50f = 1175\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Substitute from the earlier relationship:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math 25q + 50(30 - q) = 1175\">  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Solve for <i>q</i> to get the number of quarters, subtract from 30 to get the number of half-dollars.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );