document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164906>Question 1164906</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At a recent concert, souvenirs were available for the following prices:<BR>\n" );
document.write( "Sweatshirts for $65.00<BR>\n" );
document.write( "Hats for $23.00<BR>\n" );
document.write( "Key Rings for $4.00<BR>\n" );
document.write( "During a recent period, 33 items were sold for $1,149.00. If the number of sweatshirts sold was twice the number of key rings sold, find the number of each item sold.<BR>\n" );
document.write( "Let X represent the number of sweatshirts sold.<BR>\n" );
document.write( "Let Y represent the number of hats sold.<BR>\n" );
document.write( "Let Z represent the number of key rings sold<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #789343 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13216)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=789343\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "As instructed...<br><BR>\n" );
document.write( "Let X represent the number of sweatshirts sold.<BR>\n" );
document.write( "Let Y represent the number of hats sold.<BR>\n" );
document.write( "Let Z represent the number of key rings sold.<br><BR>\n" );
document.write( "Given:<br><BR>\n" );
document.write( "(1) x+y+z = 33<BR>\n" );
document.write( "(2) 65x+23y+4z = 1149<BR>\n" );
document.write( "(3) x = 2z<br><BR>\n" );
document.write( "Substitute (3) into (1) and (2) and simplify:<br><BR>\n" );
document.write( "2z+y+z = 33<BR>\n" );
document.write( "(4) y+3z = 33<br><BR>\n" );
document.write( "65(2z)+23y+4z = 1149<BR>\n" );
document.write( "(5) 23y+134z = 1149<br><BR>\n" );
document.write( "Multiply (4) by 23 and compare to (5):<br><BR>\n" );
document.write( "23y+69z = 759<BR>\n" );
document.write( "23y+134z = 1149<BR>\n" );
document.write( "65y = 390<br><BR>\n" );
document.write( "You can finish from there:<BR>\n" );
document.write( "solve the last equation for y<BR>\n" );
document.write( "substitute into (4) to solve for z<BR>\n" );
document.write( "substitute into (3) to solve for x<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );