document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184048>Question 1184048</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Vincent had some peanuts. He ate 1/4 of it last week and 2/3 of the remaining peanuts <BR>\n" );
document.write( "last night. His mother gave him another 4.14 kg of peanuts just now. Vincent then <BR>\n" );
document.write( "found that he had as much peanuts as he had at first. How many kilograms of <BR>\n" );
document.write( "peanuts did Vincent have at first? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #814586 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=814586\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> he started off with x kg of peanuts.\r<BR>\n" );
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document.write( "he ate 1/4 of them last week.\r<BR>\n" );
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document.write( "he was left with x = 1/4 * x = 3/4 * x.\r<BR>\n" );
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document.write( "he ate 2/3 of the rest last night.\r<BR>\n" );
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document.write( "he was left with 3/4 * x - 2/3 * 3/4 * x = 9/12 * x - 6/12 * x = 3/12 * x = 1/4 * x.\r<BR>\n" );
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document.write( "his mother gave him another 4.14 kg of peanuts.\r<BR>\n" );
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document.write( "he then had as many peanuts as he started with.\r<BR>\n" );
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document.write( "1/4 * x + 4.14 kg = x is the equation that models this.\r<BR>\n" );
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document.write( "subtract 1/4 * x from both sides of the equation to get:\r<BR>\n" );
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document.write( "4.14 = x - 1/4 * x = 3/4 * x.\r<BR>\n" );
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document.write( "4.14 = 3/4 * x is the equation after all the arithmetic is done.\r<BR>\n" );
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document.write( "multiply both sides of the equation by 4/3 to get:\r<BR>\n" );
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document.write( "4.14 * 4/3 = x\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = 4/3 * 4.14 = 5.52 kg.\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "to confirm, do the following.\r<BR>\n" );
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document.write( "start with 5.52 kg.<BR>\n" );
document.write( "take out 1/4 * 5.52 kg to get 4.14 kg left.<BR>\n" );
document.write( "take out 2/3 * 4.14 kg to get 1.38 kg left.<BR>\n" );
document.write( "add 4.14 kg to that to get 5.52 kg.\r<BR>\n" );
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document.write( "the solution is confirmed to be good.<BR>\n" );
document.write( "the original amount of peanuts was 5.52 kg.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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