document.write( "Question 1187253: Lindsay has forgotten the day and month of Kenny's birthday. Kenny gives her the following hints for the numeric date: The day is 6 more than four times the month. The month times the day equals miss Lindsay's favorite number, 54. When is the Kenny's birthday? \n" ); document.write( "

Algebra.Com's Answer #818199 by ikleyn(52847) $\"\"$ $\"About$

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\n" ); document.write( "Lindsay has forgotten the day and month of Kenny's birthday.
\n" ); document.write( "Kenny gives her the following hints for the numeric date:
\n" ); document.write( "The day is 6 more than four times the month.
\n" ); document.write( "The month times the day equals miss Lindsay's favorite number, 54.
\n" ); document.write( "When is the Kenny's birthday?
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document.write( "Let M be the month;  then the day is  4M+6.\r\n" );
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document.write( "The product is 54:\r\n" );
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document.write( "    M*(4M + 6) = 54.\r\n" );
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document.write( "Simplify it to\r\n" );
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document.write( "    M*(2M + 3) = 27.\r\n" );
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document.write( "Since 27 = 3^3,  we have check this possibilities for M: 1, 3, 9.\r\n" );
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document.write( "If M= 1, then  M*(2M+3) = 1*(2+3) = 5  does not work.\r\n" );
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document.write( "If M= 3, then M*(2M+3) = 3*(2*3+3) = 3*9 = 27,  and it works.\r\n" );
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document.write( "    OBVIOUSLY, at this point we can STOP our checking process.\r\n" );
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document.write( "So, the month is 3 and the day is  4M + 6 = 4*3 + 6 = 12 + 6 = 18.\r\n" );
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document.write( "ANSWER.  The birthday is  March, 18.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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