document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=679003>Question 679003</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I've already tried to solve this exam question (just by trial and error) and i got the answer is Susan pay $0.09 for each sticker and she buy 48 stickers.\r<BR>\n" );
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document.write( "But my teacher said the answer is Susan pay $0.36 for each sticker and she buy 13 stickers.\r<BR>\n" );
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document.write( "The problem is she didn't tell me the process to get it and because i just use trial and error, i also don't know the process to get my answer so i don't know whether it's correct or not.\r<BR>\n" );
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document.write( "Could you help me to solve this question with the step by step process ?<BR>\n" );
document.write( "Here's the question.\r<BR>\n" );
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document.write( "Susan paid $4.32 for a number of stickers. If the price of a sticker was cheaper by 3 cents, she could get 12 more stickers for the same amount of money. How much did she pay for each sticker and how many stickers did she buy ?<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 #421747 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=421747\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let n = number of stickers bought (before the price becomes cheaper by 3 cents) and p = price per sticker (in dollars)\r<BR>\n" );
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document.write( "\"Susan paid $4.32 for a number of stickers\" means that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2Ap+=+4.32 ALIGN=MIDDLE  ALT=\"n%2Ap+=+4.32\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solve for n to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+4.32%2Fp ALIGN=MIDDLE  ALT=\"n+=+4.32%2Fp\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "\"If the price of a sticker was cheaper by 3 cents\" tell us that if the price was really p - 0.03 dollars \"she could get 12 more stickers for the same amount of money\" means she can get n+12 stickers (instead of just n stickers)\r<BR>\n" );
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document.write( "This means that\r<BR>\n" );
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document.write( "(Number of Stickers)*(Price) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B12%29%2A%28p-0.03%29+=+4.32 ALIGN=MIDDLE  ALT=\"%28n%2B12%29%2A%28p-0.03%29+=+4.32\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Expand and simplify to get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B12%29%2A%28p-0.03%29+=+4.32 ALIGN=MIDDLE  ALT=\"%28n%2B12%29%2A%28p-0.03%29+=+4.32\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=np+-+0.03n+%2B+12p+-+0.36+=+4.32 ALIGN=MIDDLE  ALT=\"np+-+0.03n+%2B+12p+-+0.36+=+4.32\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=np+-+0.03n+%2B+12p+=+4.32+%2B+0.36 ALIGN=MIDDLE  ALT=\"np+-+0.03n+%2B+12p+=+4.32+%2B+0.36\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=np+-+0.03n+%2B+12p+=+4.68 ALIGN=MIDDLE  ALT=\"np+-+0.03n+%2B+12p+=+4.68\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+4.32%2Fp ALIGN=MIDDLE  ALT=\"n+=+4.32%2Fp\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284.32%2Fp%29p+-+0.03%284.32%2Fp%29+%2B+12p+=+4.68 ALIGN=MIDDLE  ALT=\"%284.32%2Fp%29p+-+0.03%284.32%2Fp%29+%2B+12p+=+4.68\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.32+-+0.1296%2Fp+%2B+12p+=+4.68 ALIGN=MIDDLE  ALT=\"4.32+-+0.1296%2Fp+%2B+12p+=+4.68\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.1296%2Fp+%2B+12p+=+4.68+-+4.32 ALIGN=MIDDLE  ALT=\"-0.1296%2Fp+%2B+12p+=+4.68+-+4.32\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.1296%2Fp+%2B+12p+=+0.36 ALIGN=MIDDLE  ALT=\"-0.1296%2Fp+%2B+12p+=+0.36\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Then multiply everything by the LCD p to clear out the fractions\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28-0.1296%2Fp%29+%2B+p%2A12p+=+p%2A0.36 ALIGN=MIDDLE  ALT=\"p%28-0.1296%2Fp%29+%2B+p%2A12p+=+p%2A0.36\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.1296+%2B+12p%5E2+=+0.36p ALIGN=MIDDLE  ALT=\"-0.1296+%2B+12p%5E2+=+0.36p\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.1296+%2B+12p%5E2+-+0.36p+=+0 ALIGN=MIDDLE  ALT=\"-0.1296+%2B+12p%5E2+-+0.36p+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12p%5E2+-+0.36p+-+0.1296+=+0 ALIGN=MIDDLE  ALT=\"12p%5E2+-+0.36p+-+0.1296+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The equation is now in standard form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ap%5E2%2Bbp%2Bc=0 ALIGN=MIDDLE  ALT=\"ap%5E2%2Bbp%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Use the quadratic formula to solve for p\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"p+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28-%28-0.36%29%2B-sqrt%28%28-0.36%29%5E2-4%2812%29%28-0.1296%29%29%29%2F%282%2812%29%29 ALIGN=MIDDLE  ALT=\"p+=+%28-%28-0.36%29%2B-sqrt%28%28-0.36%29%5E2-4%2812%29%28-0.1296%29%29%29%2F%282%2812%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+12 ALIGN=MIDDLE  ALT=\"a+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+-0.36 ALIGN=MIDDLE  ALT=\"b+=+-0.36\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+-0.1296 ALIGN=MIDDLE  ALT=\"c+=+-0.1296\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%280.36%2B-sqrt%280.1296-%28-6.2208%29%29%29%2F%2824%29 ALIGN=MIDDLE  ALT=\"p+=+%280.36%2B-sqrt%280.1296-%28-6.2208%29%29%29%2F%2824%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%280.36%2B-sqrt%280.1296%2B6.2208%29%29%2F%2824%29 ALIGN=MIDDLE  ALT=\"p+=+%280.36%2B-sqrt%280.1296%2B6.2208%29%29%2F%2824%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%280.36%2B-sqrt%286.3504%29%29%2F24 ALIGN=MIDDLE  ALT=\"p+=+%280.36%2B-sqrt%286.3504%29%29%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%280.36%2Bsqrt%286.3504%29%29%2F24 ALIGN=MIDDLE  ALT=\"p+=+%280.36%2Bsqrt%286.3504%29%29%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%280.36-sqrt%286.3504%29%29%2F24 ALIGN=MIDDLE  ALT=\"p+=+%280.36-sqrt%286.3504%29%29%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+0.12 ALIGN=MIDDLE  ALT=\"p+=+0.12\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+-0.09 ALIGN=MIDDLE  ALT=\"p+=+-0.09\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since a negative price doesn't make much sense, we toss out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+-0.09 ALIGN=MIDDLE  ALT=\"p+=+-0.09\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the only solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=0.12 ALIGN=MIDDLE  ALT=\"p=0.12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the price per sticker is <font color=\"red\">12 cents</font>.\r<BR>\n" );
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document.write( "Let's find n.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+4.32%2Fp ALIGN=MIDDLE  ALT=\"n+=+4.32%2Fp\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+4.32%2F0.12 ALIGN=MIDDLE  ALT=\"n+=+4.32%2F0.12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+36 ALIGN=MIDDLE  ALT=\"n+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Which means that she bought <font color=\"red\">36 stickers</font>\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "First note that buying 36 stickers at 12 cents a piece costs a total of 36*0.12 = 4.32 dollars. So that part checks out\r<BR>\n" );
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document.write( "If you lower the price 3 cents, it drops to 9 cents per sticker. We're told that you can buy 12 more stickers (or 36+12 = 48 stickers total now) and the final price won't change.\r<BR>\n" );
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document.write( "Sure enough, multiplying 0.09 by 48 will give you 0.09*48 = 4.32 and that confirms the second bit of info given.\r<BR>\n" );
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document.write( "So something doesn't fit because these two answers aren't the answers that your teacher gave you. <BR>\n" );
document.write( "Either the problem is wrong (there might be a typo in the problem) or the answer your teacher gave you is wrong (s/he might be mistaken).\r<BR>\n" );
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document.write( "So again, to sum things up, the answer is that she paid <font color=\"red\">12 cents</font> a sticker and she bought  <font color=\"red\">36 stickers</font>.<BR>\n" );
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