document.write( "Question 1024911: Carol is three times as old as John who is ten years older than Henry. The sum of their ages is 140 years. Calculate their ages. \n" ); document.write( "

Algebra.Com's Answer #640275 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "Carol is three times as old as John who is ten years older than Henry. The sum of their ages is 140 years. Calculate their ages.
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document.write( "C = 3J,           (1)     (\"Carol is three times as old as John\")\r\n" );
document.write( "J = H + 10,       (2)     (\"John . . . is ten years older than Henry\")\r\n" );
document.write( "C + J + H = 140.  (3)     (\"The sum of their ages is 140 years\")\r\n" );
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document.write( "Substitute (1) and (2) into (3). You will get\r\n" );
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document.write( "3J + (H + 10) + H = 140.   (4)\r\n" );
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document.write( "Substitute (2) into (4). You will get a single equation for H:\r\n" );
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document.write( "3*(H+10) + (H+10) + H = 140.\r\n" );
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document.write( "Simplify and solve it for H:\r\n" );
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document.write( "3H + 30 + H + 10 + H = 40,\r\n" );
document.write( "5H = 140 - 30 - 10 = 100,\r\n" );
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document.write( "H =  = 20.  It is Henry's age.\r\n" );
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document.write( "Then John is J = H + 10 = 20 + 10 = 30 years,  and\r\n" );
document.write( "C = 3J = 3*30 = 90 years for Carol.\r\n" );
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