document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1052808>Question 1052808</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "fiona is holidaying in Europe. After a week she has spent 2/5 of her spending money.  The following week she spends 630 dollars and calculates that she has 1/4 of her money left.what was her original<BR>\n" );
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document.write( "My answer was 4200 dollars the textbook solution was 1800 dollars. Who is correct?\r<BR>\n" );
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document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #668123 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=668123\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this one is tricky.\r<BR>\n" );
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document.write( "let x equal her original spending money.\r<BR>\n" );
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document.write( "after the first week she spent 2/5 of that.\r<BR>\n" );
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document.write( "what she has left is 3/5 * x.\r<BR>\n" );
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document.write( "the following week she spends 630 dollars and calculates that she has 1/4 of her spending money left.\r<BR>\n" );
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document.write( "i believe they mean 1/4 of her original spending money left.\r<BR>\n" );
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document.write( "the only way i know that is because it makes the answer come out what they said it should come out.\r<BR>\n" );
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document.write( "she starts with x.\r<BR>\n" );
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document.write( "after one week she spends 2/5 * x.\r<BR>\n" );
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document.write( "therefore she has 3/5 * x left.\r<BR>\n" );
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document.write( "after two weeks she spends an additional 630 dollars and has 1/4 * x left.\r<BR>\n" );
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document.write( "the formula for this would be 3/5 * x - 630 = 1/4 * x\r<BR>\n" );
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document.write( "solve for x as follows:\r<BR>\n" );
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document.write( "start with 3/5 * x - 630 = 1/4 * x\r<BR>\n" );
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document.write( "subtact 1/4 * x from both sides of the equation and add 630 to both sides of the equation to get 3/5 * x - 1/4 * x = 630\r<BR>\n" );
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document.write( "3/5 is equal to 12/20 and 1/4 is equal to 5/20.\r<BR>\n" );
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document.write( "the equation becomes 12/20 * x - 5/20 * x = 630\r<BR>\n" );
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document.write( "combine like terms to get 7/20 * x = 630\r<BR>\n" );
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document.write( "solve for x to get x = 20/7 * 630 = 1800.\r<BR>\n" );
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document.write( "if the original amount is 1800, then she spent 2/5 of that.\r<BR>\n" );
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document.write( "this means she spent 720 dollars.\r<BR>\n" );
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document.write( "1800 - 710 = means she had 1080 left.\r<BR>\n" );
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document.write( "she then spent 630 which means she had 1080 - 630 = 450 left.\r<BR>\n" );
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document.write( "450 is equal to 1/4 * 1800.\r<BR>\n" );
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document.write( "if the original amount is 4200, and she spent 2/5 of that in the first week, then she had 3/5 * 4200 = 2520 left.\r<BR>\n" );
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document.write( "she then spent 630 which means she had 1890 left.\r<BR>\n" );
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document.write( "1890 is not equal to 1/4 * 4200.\r<BR>\n" );
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document.write( "doesn't compute.\r<BR>\n" );
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document.write( "if you can explain to me how you got 4200 then i might be able to explain to you what you did wrong.\r<BR>\n" );
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document.write( "i think what you might have done is say that 2/5 * x was remaining.\r<BR>\n" );
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document.write( "if that's the case, then you would get 2/5 * x - 630 = 1/4 * x.\r<BR>\n" );
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document.write( "if you solved for x in that case, then you would get 4200.\r<BR>\n" );
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document.write( "unfortunately, what remained after the first week was 3/5 * x and not 2/5 * x.\r<BR>\n" );
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document.write( "2/5 * x is what was spent in the first week.\r<BR>\n" );
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document.write( "i give it to the book this time.<BR>\n" );
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