document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1081202>Question 1081202</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If I just sold my two books at $990 each. On one I gained 10% and on the other one I lost 10%. Then.<BR>\n" );
document.write( "(a) I lost $20.<BR>\n" );
document.write( "(b) I gained $918.<BR>\n" );
document.write( "(c) I gained $19.8.<BR>\n" );
document.write( "(d) None of these. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #695246 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=695246\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let<BR>\n" );
document.write( "x = original value of book1<BR>\n" );
document.write( "y = original value of book2<BR>\n" );
document.write( "this is at the point in time when you are buying each book (not selling)\r<BR>\n" );
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document.write( "you bought book1 for x dollars and turn around to sell it for 990 dollars. The difference in price is 990-x which is some positive number (since you gain money for selling this book). \r<BR>\n" );
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document.write( "Divide this difference over the original price x to get (990-x)/x. This ratio will result in the decimal value 0.10 which represents a 10% gain. So we have this equation (990-x)/x = 0.10\r<BR>\n" );
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document.write( "Let's solve for x<BR>\n" );
document.write( "(990-x)/x = 0.10<BR>\n" );
document.write( "x*(990-x)/x = x*0.10<BR>\n" );
document.write( "990-x = 0.10x<BR>\n" );
document.write( "990-x+x = 0.10x+x<BR>\n" );
document.write( "990 = 1.10x<BR>\n" );
document.write( "1.10x = 990<BR>\n" );
document.write( "1.10x/(1.10) = 990/(1.10)<BR>\n" );
document.write( "x = 900\r<BR>\n" );
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document.write( "So the original value of book1 is $900. This is the value in which you buy it at.\r<BR>\n" );
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document.write( "In other words, you bought book1 for $900 and sold it $990.\r<BR>\n" );
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document.write( "Similarly, the second equation would be <BR>\n" );
document.write( "(990-y)/y = -0.10<BR>\n" );
document.write( "Notice how the right hand side is negative to indicate a loss. The left side is identical to the first equation (use y instead of x).\r<BR>\n" );
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document.write( "Solve for y<BR>\n" );
document.write( "(990-y)/y = -0.10<BR>\n" );
document.write( "y*(990-y)/y = y*(-0.10)<BR>\n" );
document.write( "990-y = -0.10y<BR>\n" );
document.write( "990-y+y = -0.10y+y<BR>\n" );
document.write( "990 = 0.90y<BR>\n" );
document.write( "0.90y = 990<BR>\n" );
document.write( "0.90y/(0.90) = 990/(0.90)<BR>\n" );
document.write( "y = 1100\r<BR>\n" );
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document.write( "So you bought book2 for $1100 and then later sold it for $990. \r<BR>\n" );
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document.write( "Recapping so far:<BR>\n" );
document.write( "<ul><li>you buy book1 for $900 and sell it later for $990.</li></ul><BR>\n" );
document.write( "<ul><li>you buy book2 for $1100 and sell it later for $990.</li></ul>\r<BR>\n" );
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document.write( "In the case of book1, you have a profit of <BR>\n" );
document.write( "(new value) - (old value) = 990-900 = 90 dollars\r<BR>\n" );
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document.write( "In the case of book2, you have a profit of <BR>\n" );
document.write( "(new value) - (old value) = 990-1100 = -110 dollars<BR>\n" );
document.write( "Note: the negative profit means a loss\r<BR>\n" );
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document.write( "The two profits (90 and -110) are then combined to get this overall net profit: 90 + (-110) = -20\r<BR>\n" );
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document.write( "At the end of the day, the net profit comes out to -20 dollars indicating that you lost $20. \r<BR>\n" );
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document.write( "Answer: <font color=red>Choice (a) I lost $20</font> </SPAN>\n" );
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