document.write( "Question 1097559: If the larger of two numbers is divided by the smaller, the quotient is 7 and the remainder is 19. But if 3 times the greater is divided by twice the smaller, the quotient is 11 and the remainder is 19. What are the numbers? \n" ); document.write( "

Algebra.Com's Answer #712002 by ikleyn(52786) $\"\"$ $\"About$

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document.write( "Let x be the larger of the two numbers and y be the smaller.\r\n" );
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document.write( "Then the condition gives you these two equations\r\n" );
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document.write( "x = 7y + 19,           (1)\r\n" );
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document.write( "3x = 11*(2y) + 19.     (2)\r\n" );
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document.write( "Substitute (1) into (2). You will get\r\n" );
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document.write( "3*(7y + 19) = 22y + 19,    or\r\n" );
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document.write( "21y + 57 = 22y + 19  ====>  y = 57 - 19 = 38.\r\n" );
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document.write( "Then  x = 7*y + 19 = 7*38 + 19 = 285.\r\n" );
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document.write( "Answer.  The larger number is 285.  The smaller number is 38.\r\n" );
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document.write( "Check.   Check eq(1):  7*y+19 = 7*38+19 = 285 = x.             ! Correct !\r\n" );
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document.write( "         Check eq(2):  3x = 3*285 = 11*2*38+19 = 11*(2x)+19.   ! Correct !\r\n" );
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\n" ); document.write( "\n" ); document.write( "Thanks to @MathTherapy for pointing my error in the earlier version.\r
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