Question 1187253
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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?
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<pre>
Let M be the month;  then the day is  4M+6.


The product is 54:

    M*(4M + 6) = 54.


Simplify it to

    M*(2M + 3) = 27.


Since 27 = 3^3,  we have check this possibilities for M: 1, 3, 9.


If M= 1, then  M*(2M+3) = 1*(2+3) = 5  does not work.


If M= 3, then M*(2M+3) = 3*(2*3+3) = 3*9 = 27,  and it works.



    OBVIOUSLY, at this point we can STOP our checking process.



So, the month is 3 and the day is  4M + 6 = 4*3 + 6 = 12 + 6 = 18.


<U>ANSWER</U>.  The birthday is  March, 18.
</pre>

Solved.