document.write( "Question 1173031: Five years ago Barbra was four-fifths Bill's age then. In ten years she will be
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Algebra.Com's Answer #798207 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
Five years ago Barbra was four-fifths Bill's age then. In ten years she will be
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document.write( "You omitted the question which obviously was \"How old are they now?\"  Ikleyn\r\n" );
document.write( "gets all bent outta shape when students leave out anything.  I don't.  But\r\n" );
document.write( "instead of doing your problem for you, I'll do one exactly like it step-by-\r\n" );
document.write( "step.  Here is the problem I will do for you:\r\n" );
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Seven years ago Barbra was two-thirds Bill's age then. In four years she will
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document.write( "Let x = Barbra's age now\r\n" );
document.write( "Let y = Bill's age now\r\n" );
document.write( "Then x-7 = Barbra's age 7 years ago\r\n" );
document.write( "Then y-7 = Bill's age 7 years ago\r\n" );
document.write( "Also x+4 = Barbra's age 4 years from now\r\n" );
document.write( "Also y+4 = Bill's age 4 years from now\r\n" );
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Seven years ago Barbra was two-thirds Bill's age then.
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document.write( "\"x-7+=+expr%282%2F3%29%28y-7%29\"\r\n" );
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In four years she will be three-fourths his age then.
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document.write( "\"x%2B4+=+expr%283%2F4%29%28x%2B4%29\"\r\n" );
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document.write( "The system you are to solve is\r\n" );
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document.write( "\"system%28x-7+=+expr%282%2F3%29%28y-7%29%2Cx%2B4+=+expr%283%2F4%29%28y%2B4%29%29\"\r\n" );
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document.write( "Multiply the first equation through by 3 and the second one through by 4 to\r\n" );
document.write( "clear the fractions:\r\n" );
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document.write( "\"system%283x-21+=+2%28y-7%29%2C4x%2B16+=+3%28y%2B4%29%29\"\r\n" );
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document.write( "Distribute the right sides:\r\n" );
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document.write( "\"system%283x-21+=+2y-14%2C4x%2B16+=+3y%2B12%29\"\r\n" );
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document.write( "Rearrange the terms:\r\n" );
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document.write( "\"system%283x-2y=7%2C4x-3y=-4%29\"\r\n" );
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document.write( "To eliminate y, multiply the first equation by -3 and the second equation by 2:\r\n" );
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document.write( "\"system%28-9x%2B6y=-21%2C8x-6y=-8%29\"\r\n" );
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document.write( "Add term-by-term to eliminate the y-terms\r\n" );
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document.write( "\"-x=-29\"\r\n" );
document.write( "\"x=29\", So Barbra is 29    \r\n" );
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document.write( "Substitute in \r\n" );
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document.write( "\"3x-2y=7%29\"\r\n" );
document.write( "\"3%2829%29-2y=7%29\"\r\n" );
document.write( "\"87-2y=7\"\r\n" );
document.write( "\"-2y=-80\"\r\n" );
document.write( "\"y=40\", so Bill is 40.\r\n" );
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document.write( "Checking:\r\n" );
document.write( "Seven years ago Barbra was 29-7=22\r\n" );
document.write( "Seven years ago Bill was 40-7=33\r\n" );
document.write( "Indeed, 22 is 2/3 of 33.  That checks.\r\n" );
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document.write( "In four years, Barbra will be 29+4=33\r\n" );
document.write( "In four years, Bill will be 40+4=44\r\n" );
document.write( "Indeed, 33 is 3/4 of 44.  That checks.\r\n" );
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document.write( "Now do your problem the exact same way step by step, using this as a guide.\r\n" );
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document.write( "Edwin
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