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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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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.
ANSWER. The birthday is March, 18.
Solved.