document.write( "Question 1158138: The product of the present ages of a mother and her daughter is 432. Four years ago the mother was exactly four times as old as the daughter .what are their present ages? \n" ); document.write( "

Algebra.Com's Answer #781043 by ikleyn(52803) $\"\"$ $\"About$

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document.write( "Let x be the present age of the daughter.\r\n" );
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document.write( "Then  the present age of the mother is 4*(x-4)+4 = 4x - 12.\r\n" );
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document.write( "From the condition, you have this equation\r\n" );
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document.write( "    x*(4x-12) = 432.\r\n" );
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document.write( "Cancel the factor 4 in both sides\r\n" );
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document.write( "    x*(x-3) = 108.\r\n" );
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document.write( "You can solve this quadratic equation.\r\n" );
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document.write( "An alternative way is to decompose MENTALLY the number 108 into the product of two factors with the difference 3 between them \r\n" );
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document.write( "    108 = 9*12,\r\n" );
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document.write( "so the answer is the greater of these two factors x= 12.\r\n" );
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document.write( "ANSWER.  The daughter is 12 years old.  The mother is 4x - 12 = 4*12-12 = 36 years old.\r\n" );
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document.write( "CHECK.  12*36 = 432.   ! Correct !\r\n" );
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