document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1139492>Question 1139492</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mark won a lottery and received $74,000; he invested part of it in his retirement account and donated the rest to a charity.  The amount of the donation was $500 less than a quarter of the amount of the investment.  How much did Mark invest in his retirement account and how much did he donate to the charity?\r<BR>\n" );
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document.write( "(a)   Define your variable(s).\r<BR>\n" );
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document.write( "(b)   Construct a mathematical model (equation) in one unknown.\r<BR>\n" );
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document.write( "(c)   Solve the equation constructed. \r<BR>\n" );
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document.write( "(d)   Write a sentence to represent your findings </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #759982 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=759982\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mark wins the lottery and receives 74,00.<BR>\n" );
document.write( "he invest part of it and donates the rest to charity.<BR>\n" );
document.write( "the amount he donates is 500 less than a quarter of the amount of the investment.<BR>\n" );
document.write( "how much did he invest in his retirement account and how much did he donate to charity.\r<BR>\n" );
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document.write( "let x equal the amount he donated to charity.<BR>\n" );
document.write( "74,000 is the amount he received.<BR>\n" );
document.write( "the amount he donated is 500 less than one quarter of the amount of the investment.\r<BR>\n" );
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document.write( "if we let x equal the amount he donaterd to charity and if we let y equal the amount he invested, we get:\r<BR>\n" );
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document.write( "x + y = 74,000<BR>\n" );
document.write( "x = 1/4 * y - 500\r<BR>\n" );
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document.write( "replace x with 1/4 * y - 500 in the equation of x + y = 74,000 to get:\r<BR>\n" );
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document.write( "1/4 * y - 500 + y = 74,000\r<BR>\n" );
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document.write( "add 500 to both sides of this equation to get 1/4 * y + y = 74,500.\r<BR>\n" );
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document.write( "combine like terms to get 5/4 * y = 74,500\r<BR>\n" );
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document.write( "solve for y to get y = 74,500 * 4/5 = 59,600.\r<BR>\n" );
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document.write( "since x + y = 74,000, then x must be equal to 74,000 - 59,600 = 14,400.\r<BR>\n" );
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document.write( "it appears that your solution is that he invested 59,600 in his retirement account and he donated 14,400 to charity.\r<BR>\n" );
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document.write( "all we need to do is to confirm that this is correct.\r<BR>\n" );
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document.write( "x + y = 74,000 becomes 14,400 + 59,600 = 74,000 which is true.\r<BR>\n" );
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document.write( "x = 1/4 * y - 500 becomes x = 1/4 * 59,600 - 500 which becomes x = 14,400 which is true.\r<BR>\n" );
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document.write( "the solution looks good.\r<BR>\n" );
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document.write( "the solution is that he invested 59,600 in his retirement account and donates 14,400 to charity.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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