document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209350>Question 1209350</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Rama was getting some items for the new school year. First, he bought some textbooks with $8 more than 1/3 of his money. Next, Next, he bought his stationery with $12.20 less than 1/2 of his remaining money. Lastly, he bought some school socks with $2.80 more than 1/2 of the money left. Then, he had $15.40 with him. How much money did he have at first? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848622 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=848622\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Working the problem \"forwards\", as shown in the other responses, requires doing some back-substitution to get the final answer.<br><BR>\n" );
document.write( "You can get the answer directly by working the problem backwards.<br><BR>\n" );
document.write( "He finished with $15.40 after spending $2.80 more than half of his money on school socks.<br><BR>\n" );
document.write( "let x = amount he had before buying the socks<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-%28%281%2F2%29x%2B2.80%29=15.40 ALIGN=MIDDLE  ALT=\"x-%28%281%2F2%29x%2B2.80%29=15.40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29x-2.80=15.40 ALIGN=MIDDLE  ALT=\"%281%2F2%29x-2.80=15.40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29x=18.20 ALIGN=MIDDLE  ALT=\"%281%2F2%29x=18.20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=36.40 ALIGN=MIDDLE  ALT=\"x=36.40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Before buying the socks, the amount he had was $36.40.  That was what he had after spending $12.20 less than half his money on stationery.<br><BR>\n" );
document.write( "let y = amount he had before buying the stationery<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-%28%281%2F2%29y-12.20%29=36.40 ALIGN=MIDDLE  ALT=\"y-%28%281%2F2%29y-12.20%29=36.40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29y%2B12.20=36.40 ALIGN=MIDDLE  ALT=\"%281%2F2%29y%2B12.20=36.40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29y=24.20 ALIGN=MIDDLE  ALT=\"%281%2F2%29y=24.20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=48.40 ALIGN=MIDDLE  ALT=\"y=48.40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The amount he had before buying the stationery was $48.40.  That was what he had after spending $8 more than 1/3 of his money on textbooks.<br><BR>\n" );
document.write( "let z = amount he had before buying the textbooks (i.e., the amount he had at first)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z-%28%281%2F3%29z%2B8%29=48.40 ALIGN=MIDDLE  ALT=\"z-%28%281%2F3%29z%2B8%29=48.40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29z-8=48.40 ALIGN=MIDDLE  ALT=\"%282%2F3%29z-8=48.40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29z=56.40 ALIGN=MIDDLE  ALT=\"%282%2F3%29z=56.40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=84.60 ALIGN=MIDDLE  ALT=\"z=84.60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: The amount he started with was $86.40<br><BR>\n" );
document.write( " </SPAN>\n" );
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