document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=581274>Question 581274</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A teacher must buy 100 treats for exactly $100.  Chocolate costs $0.56 each, cupcakes cost $0.92 each, and large cakes cost $2.26 each.  How many of each does she buy to have a total of 100 for $100? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #371605 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=371605\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A teacher must buy 100 treats for exactly $100.<BR>\n" );
document.write( " Chocolate costs $0.56 each, cupcakes cost $0.92 each, and large cakes cost $2.26 each. <BR>\n" );
document.write( "How many of each does she buy to have a total of 100 for $100?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "we got 3 unknowns, and only two equations, calls for some help from our calc<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let a = no. of Chocolates<BR>\n" );
document.write( "Let b = no. of cupcakes<BR>\n" );
document.write( "Let c = no. of large cakes<BR>\n" );
document.write( ":<BR>\n" );
document.write( "a + b + c = 100<BR>\n" );
document.write( ":<BR>\n" );
document.write( ".56a + .92b + 2.26c = 100.00<BR>\n" );
document.write( "multiply by 100 to get rid of the decimals<BR>\n" );
document.write( "56a + 92b + 226c = 10000<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Multiply the 1st equation by 56, subtract from the above equation<BR>\n" );
document.write( "56a + 92b + 226c = 10000<BR>\n" );
document.write( "56a + 56b + 56c =   5600<BR>\n" );
document.write( "----------------------------subtraction eliminates a<BR>\n" );
document.write( "0a + 36b + 170c = 4400<BR>\n" );
document.write( "36b = -170c + 4400<BR>\n" );
document.write( "divide by 36, reduce the fractions<BR>\n" );
document.write( "b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-85%2F18 ALIGN=MIDDLE  ALT=\"-85%2F18\"   DISABLED_style= \"max-width:90%; height:auto;\" >c + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1100%2F9 ALIGN=MIDDLE  ALT=\"1100%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Only one integer solution for this equation (used the table on a Ti83)<BR>\n" );
document.write( "c = 10 cakes<BR>\n" );
document.write( "b = 75 cupcakes<BR>\n" );
document.write( "then<BR>\n" );
document.write( "a = 100 - 85<BR>\n" );
document.write( "a = 15 chocolate<BR>\n" );
document.write( ":<BR>\n" );
document.write( "See if this checks out by finding total cost <BR>\n" );
document.write( ".56(15)  = 8.40<BR>\n" );
document.write( ".92(75) = 69.00<BR>\n" );
document.write( "2.26(10)= 22.60<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "total$ = $100.00 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );