document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=842183>Question 842183</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mr. Ray handed the bank teller a check for $260 and said,\"I wish three times as many one-dollars bills as fives, and half as many tens as fives,\" What should the teller have given him </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #507422 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=507422\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> o = number of one dollar bills.<BR>\n" );
document.write( "t = number of ten dollar bills.<BR>\n" );
document.write( "f = number of five dollar bills.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in terms of dollars.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "each one is worth one dollar.<BR>\n" );
document.write( "each ten is worth 10 dollars.<BR>\n" );
document.write( "each 5 is worth 5 dollars.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in terms of value, then:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "o + 5f + 10t = 260 dollars.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that translates to the number of one dollars bills times 1 plus the number of 5 dollars bills times 5 plus the number of 10 dollar bills plus 10 times the number of 10 dollars bills is equal to 260 dollars.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the statement:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "\"I wish three times as many one-dollars bills as fives, and half as many tens as fives,\"\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "translates to:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "o = 3f<BR>\n" );
document.write( "this means that the number of one dollar bills is three times the number of five dollar bills.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "t = f/2<BR>\n" );
document.write( "this means that the number of ten dollar bills is 1/2 times the number of five dollar bills.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "start with the general equation of:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "o + 5f + 10t = 260\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "replace o with 3f to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "3f + 5f + 10t = 260\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "replace t with f/2 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "3f + 5f + 10f/2 = 260.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "3f + 5f + 5f = 260.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "combine like terms to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "13f = 260\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide both sides of the equation by 13 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f = 260 / 13 = 20\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since t = f/2, then t = 10\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since o = 3f, then o = 60\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you get:<BR>\n" );
document.write( "o = 60<BR>\n" );
document.write( "f = 20<BR>\n" );
document.write( "t = 10\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the general equation of o + 5f + 10t = 260 becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "60 + 5*20 + 10*10 = 260 becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "60 + 100 + 100 = 260 which becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "260 = 260 which confirms the solutions is good.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you have 60 ones, 20 fives, and 10 tens.<BR>\n" );
document.write( "the number of ones is equal to 3 times the number of fives.<BR>\n" );
document.write( "the number of tens is equal to 1/2 times the number of fives.<BR>\n" );
document.write( "the sum of the dollar value is equal to 260.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );