document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182797>Question 1182797</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When the price of an item was increased by sh.5, I bought 2 items fewer with sh.200. <BR>\n" );
document.write( "what is the current price of the item?    (It's a kcse question on 1994 pp1 no.16)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #812871 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=812871\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The number you can buy for sh.200 is 200 divided by the price.<br><BR>\n" );
document.write( "The new price is sh.5 more than the old, so<br><BR>\n" );
document.write( "let x = old price<BR>\n" );
document.write( "then x+5 = new price<br><BR>\n" );
document.write( "The number you can buy at the new price is 2 less than the number you could buy at the old price:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%2F%28x%2B5%29+=+200%2Fx-2 ALIGN=MIDDLE  ALT=\"200%2F%28x%2B5%29+=+200%2Fx-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Multiply everything by the least common denominator to clear fractions:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%28x%29=200%28x%2B5%29-2%28x%28x%2B5%29%29 ALIGN=MIDDLE  ALT=\"200%28x%29=200%28x%2B5%29-2%28x%28x%2B5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200x+=+200x%2B1000-2x%5E2-10x ALIGN=MIDDLE  ALT=\"200x+=+200x%2B1000-2x%5E2-10x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B10x-1000+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B10x-1000+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B5x-500+=+0 ALIGN=MIDDLE  ALT=\"x%5E2%2B5x-500+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B25%29%28x-20%29+=+0 ALIGN=MIDDLE  ALT=\"%28x%2B25%29%28x-20%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "x=-25 or x=20; obviously the negative number makes no sense in the problem, so x=20.<br><BR>\n" );
document.write( "The problem asks for the \"current\" (new) price, which is x+5=25.<br><BR>\n" );
document.write( "ANSWER: The current price is sh.25.<br><BR>\n" );
document.write( "Knowing how to solve the problem using formal algebra is important.  But if this is a question on a competitive math exam, it's much faster to solve the problem informally.<br><BR>\n" );
document.write( "To do that, write out (on paper if needed; or just in your mind) a list of all the pairs of positive integers whose product is 200; then look for two of those pairs in which one of the numbers differs by 2 and the other differs by 5.<br><BR>\n" );
document.write( "1 * 200<BR>\n" );
document.write( "2 * 100<BR>\n" );
document.write( "4 * 50<BR>\n" );
document.write( "5 * 40<BR>\n" );
document.write( "8 * 25<BR>\n" );
document.write( "10 * 20<br><BR>\n" );
document.write( "Look at the last two pairs.  The 8 and 10 differ by 2; the 25 and 20 differ by 5.<br><BR>\n" );
document.write( "That gives you your answer.  For sh.200, you can buy 8 of the items at sh.25 each or 10 of them at sh.20 each.  So the current price, at which you can buy 2 fewer of the items than before, is sh.25.<br><BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );