Question 9360
let the 2-digit number be thought of as xy. This means the number is really 10x+y, as 34 means 30+4--> 3x10 + 4


Product is xy = 12 --eqn1


straightaway, this means we have either 26 or 34. Looking at these, adding 36 to both gives 62 or 70. So the answer is 26.


Anyway, algebraically...


adding 36 to the number is 10x+y+36
and this equals "yx" or rather 10y+x


so, 10x+y+36 = 10y+x
--> 9x - 9y = -36
--> x - y = -4


and subbing in eqn1 into this gives {{{12/y - y = -4}}}


{{{12 - y^2 = -4y}}}
{{{y^2 - 4y - 12 = 0}}}
(y+2)(y-6) = 0
so y = -2 or y=6


ignore the -2 value...we are looking for a positive number, so y=6. Hence from eqn1, x = 2...number is 26!


jon.