document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209504>Question 1209504</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "Jamie spent 3/4 of her money on 3 books of the same price. Grace spent 5/9 of her money on 2 diaries. They were each left with an equal amount of money. One book cost $3.30 more than one diary. How much money did they have altogether.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849012 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13206)</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=849012\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Another bizarre and incorrect AI solution from that pseudo-tutor....<br><BR>\n" );
document.write( "\"Since they had the same amount of money left, the fractions of money they spent must be equal\"<br><BR>\n" );
document.write( "That makes no logical sense.  And, besides, the statement of the problem tells us the fractions of their money that each spent, and they are not equal.<br><BR>\n" );
document.write( "Following is a logical and correct solution from a human tutor....<br><BR>\n" );
document.write( "Let J and G respectively represent the amounts of money Jamie and Grace started with.<br><BR>\n" );
document.write( "Let x be the cost of each diary; then the cost of each book was x+$3.30.<br><BR>\n" );
document.write( "Jamie spent 3/4 of her money, so she finished with 1/4 of what she started with.<br>  Grace spent 5/9 of her money, so she finished with 4/9 of what she started with.<br><BR>\n" );
document.write( "They finished with the same amounts of money:<br><BR>\n" );
document.write( "[1] <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29J=%284%2F9%29G ALIGN=MIDDLE  ALT=\"%281%2F4%29J=%284%2F9%29G\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Jamie spent 3/4 of her money on 3 books:<br><BR>\n" );
document.write( "[2] <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F4%29J=3%28x%2B3.30%29 ALIGN=MIDDLE  ALT=\"%283%2F4%29J=3%28x%2B3.30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Grace spent 5/9 of her money on 2 diaries:<br><BR>\n" );
document.write( "[3] <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2F9%29G=2%28x%29 ALIGN=MIDDLE  ALT=\"%285%2F9%29G=2%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The amount of money Jamie had left was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29%2F%283%2F4%29=1%2F3 ALIGN=MIDDLE  ALT=\"%281%2F4%29%2F%283%2F4%29=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > of what she spent:<br><BR>\n" );
document.write( "[4] <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%283%28x%2B3.30%29%29=x%2B3.30 ALIGN=MIDDLE  ALT=\"%281%2F3%29%283%28x%2B3.30%29%29=x%2B3.30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The amount of money Grace had left was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F9%29%2F%285%2F9%29=4%2F5 ALIGN=MIDDLE  ALT=\"%284%2F9%29%2F%285%2F9%29=4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > of what she spent:<br><BR>\n" );
document.write( "[5] <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F5%29%282%28x%29%29=%288%2F5%29x ALIGN=MIDDLE  ALT=\"%284%2F5%29%282%28x%29%29=%288%2F5%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The amounts they ended up with were the same:<br><BR>\n" );
document.write( "[6] <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3.30=%288%2F5%29x ALIGN=MIDDLE  ALT=\"x%2B3.30=%288%2F5%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.30=%283%2F5%29x ALIGN=MIDDLE  ALT=\"3.30=%283%2F5%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5.50 ALIGN=MIDDLE  ALT=\"x=5.50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The cost of each diary was x=$5.50; the cost of each book was x+$3.30 = $8.80.<br><BR>\n" );
document.write( "Jamie ended up with x+$3.30 = $8.80; that was 1/4 of what she started with, so she started with 4($8.80) = $35.20.<br><BR>\n" );
document.write( "Grace ended up with was (8/5)x = $8.80; that was 4/9 of what she started with, so she started with (9/4)($8.80) = 9($2.20) = $19.80.<br><BR>\n" );
document.write( "The total the two of them started with together was $35.20+$19.80 = $55.<br><BR>\n" );
document.write( "ANSWER: $55<br><BR>\n" );
document.write( "Summary....<BR>\n" );
document.write( "Jamie started with $35.20 and spent 3/4 of it ($26.40) on 3 books costing $8.80 each, finishing with 1/4 of $35.20, or $8.80.<BR>\n" );
document.write( "Grace started with $19.80 and spent 5/9 of it ($11.00) on 2 diaries costing $5.50 each, finishing with 4/9 of $19.80, or $8.80.<BR>\n" );
document.write( "The two of them finished with equal amounts.<br><BR>\n" );
document.write( " </SPAN>\n" );
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