document.write( "Question 828378: On a number line, points A, B, and C have coordinates a, b, and c with a < b < c . If
\n" ); document.write( "b = 6, AC =30, and AB = 2BC , what are the values of a and c? \n" ); document.write( "

Algebra.Com's Answer #499292 by Edwin McCravy(20060) $\"\"$ $\"About$

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document.write( "Given: b = 6, AC = 30, and AB = 2BC\r\n" );
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document.write( "Therefore AB = b-a, BC = c-b, AC = c-a  \r\n" );
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document.write( " A                   B         C\r\n" );
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document.write( "a=?                 b=6       c=?\r\n" );
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document.write( "  AB = 2BC                AC = 30\r\n" );
document.write( " b-a = 2(c-b)            c-a = 30\r\n" );
document.write( " 6-a = 2(c-6)\r\n" );
document.write( " 6-a = 2c-12\r\n" );
document.write( "  18 = 2c+a\r\n" );
document.write( "2c+a = 18\r\n" );
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document.write( "So we have the system of two equations in two unknowns:\r\n" );
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document.write( "Add the two equations and the a's cancel:\r\n" );
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document.write( "     3c = 48\r\n" );
document.write( "      c = 16\r\n" );
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document.write( "Substitute in \r\n" );
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document.write( "   2c+a = 18\r\n" );
document.write( "2(16)+a = 18\r\n" );
document.write( "   32+a = 18\r\n" );
document.write( "      a = -14\r\n" );
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document.write( "Edwin

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