document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189317>Question 1189317</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mia has a certain amount of money. If she buys 4 pens and 1 pencil, she will have $5 left over. If she buys 2 pens and 2 pencils, she will have $3 left over. If Edward arrives with the same amount of money as Mia, together they can buy 7 pens and 4 pencils and spend all their money. If a is the cost of one pen and b is the cost of one pencil, compute the ordered pair (a,b). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #820648 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</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=820648\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "When Mia buys 4 pens and 1 pencil, she has $5 left; the number of dollars she starts with is 4a+b+5.<br><BR>\n" );
document.write( "When she buys 2 pens and 2 pencils, she has $3 left; the number of dollars she starts with is 2a+2b+3.<br><BR>\n" );
document.write( "Since those two expressions represent the same number, set them equal to each other and simplify to get an equation in a and b.<br><BR>\n" );
document.write( "4a+b+5=2a+2b+3<BR>\n" );
document.write( "2a-b=-2 [1]<br><BR>\n" );
document.write( "If Edward arrives with the same number of dollars that Mia started with, they can buy 7 pens and 4 pencils with all their money.<br><BR>\n" );
document.write( "The total amount of money the two of them have is twice what Mia started with; and with that amount of money they can buy 7 pens and 4 pencils with no money left.  Write an equation that says that and simplify to get a second equation in a and b.<br><BR>\n" );
document.write( "8a+2b+10=7a+4b<BR>\n" );
document.write( "a-2b=-10 [2]<br><BR>\n" );
document.write( "Solve the pair of equations [1] and [2] by your favorite method.<br><BR>\n" );
document.write( "I'll let you choose the method to use and work the problem to find the answer.<br><BR>\n" );
document.write( "(Note: you should end up with the probably unreasonable answer that each pen costs $2 and each pencil costs $6....)<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );