document.write( "Question 1144020: Charles is 4 years older than Jake. The product of Charles' age three years from now and Jake's age 2 years ago is 90. Find their present age. \n" ); document.write( "

Algebra.Com's Answer #764978 by ikleyn(52792) $\"\"$ $\"About$

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document.write( "Let x be the Charles' age.  Then the Jake's age is (x-4).\r\n" );
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document.write( "Charles' age 3 years from now will be (x+3) years; Jake's age 2 years ago was ((x-4)-2) = (x-6) years.\r\n" );
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document.write( "We are given\r\n" );
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document.write( "     (x+3)*(x-6) = 90.\r\n" );
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document.write( "You can solve this quadratic equation using the quadratic formula.\r\n" );
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document.write( "Or you can solve it MENTALLY noticing that 90 is the product of the two factors (x+3)  and  (x-6), that differ by 9.\r\n" );
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document.write( "Then you get momentarily  x-6 = 6;  x+3 = 15,  which implies  x = 12.\r\n" );
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document.write( "ANSWER.  Charles is 12 years old;  Jake is 8 years old.\r\n" );
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document.write( "CHECK.   (12+3)*(8-2) = 15*6 = 90.    ! Correct !\r\n" );
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