document.write( "Question 174520: Jane is as old as Joan was when Jane was half as old as Joan is now. Four years ago, Jane was as old as Joan was when Jane was a third as old as Joan is now. How old will Jane be in two years?
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Algebra.Com's Answer #129526 by Edwin McCravy(20056)\"\" \"About 
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Jane is as old as Joan was when Jane was half as old as Joan is now. Four years ago, Jane was as old as Joan was when Jane was a third as old as Joan is now. How old will Jane be in two years?
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document.write( "Let \"x\" = Jane's age now\r\n" );
document.write( "Let \"y\" = Joan's age now\r\n" );
document.write( "Let \"n\" = the number of years ago when Jane \r\n" );
document.write( "              was half as old Joan is now.\r\n" );
document.write( "Let \"m\" = the number of years ago when Jane \r\n" );
document.write( "              was a third as old as Joan is now. \r\n" );
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document.write( "Jane, who is now \"x\", is as old as Joan was\r\n" );
document.write( "\"n\" years ago, \"%28y-n%29\". \r\n" );
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document.write( "That gives us the equation \"x+=+y-n\"\r\n" );
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document.write( "Also, \"n\" years ago, Jane was \"%28x-n%29\", \r\n" );
document.write( "and that was half as old as Joan is now, that \r\n" );
document.write( "is, half of \"y\".\r\n" );
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document.write( "That gives us the equation \"x-n+=+%281%2F2%29y\"\r\n" );
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document.write( "Four years ago, Jane was \"%28x-4%29\" and was as \r\n" );
document.write( "old as Joan was m years ago, or \"%28y-m%29\", \r\n" );
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document.write( "\"x-4+=+y-m\"\r\n" );
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document.write( "Also, m years ago, Jane was \"%28x-m%29\", which \r\n" );
document.write( "was one-third as old as Joan is now, or \"%281%2F3%29y\". \r\n" );
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document.write( "That gives us the equation \"x-m+=+%281%2F3%29y\"\r\n" );
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document.write( "\"system%28x+=+y-n%2C%0D%0Ax-n+=+%281%2F2%29y%2C%0D%0Ax-4+=+y-m%2C%0D%0Ax-m+=+%281%2F3%29y%29\"\r\n" );
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document.write( "Can you simplify and solve that system of equation?\r\n" );
document.write( "If you can't, post again asking how.\r\n" );
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document.write( "Solution:  \r\n" );
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document.write( "Checking:\r\n" );
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document.write( "Jane, who is now 18, is as old as Joan, \r\n" );
document.write( "who is now 24, was 6 years ago. That checks because \r\n" );
document.write( "she was indeed 18 6 years ago.  \r\n" );
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document.write( "Also, 6 years ago, Jane, who is now 18 was 12, and \r\n" );
document.write( "that was half as old as Joan is now, that is, half \r\n" );
document.write( "of 24, or 12.  That checks.\r\n" );
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document.write( "Four years ago, Jane, who is now 18 was 14 and was \r\n" );
document.write( "as old as Joan, who is now 24, was 10 years ago, or \r\n" );
document.write( "14,  That checks \r\n" );
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document.write( "Also, 10 years ago, Jane was 8, which was one-third \r\n" );
document.write( "as old as Joan is now, or 24.  That checks because 8 \r\n" );
document.write( "is one-third of 24.\r\n" );
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\n" ); document.write( "How old will Jane be in two years?
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document.write( "She's 18 now, so, in two years she'll be 20.\r\n" );
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document.write( "Edwin
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