SOLUTION: A two-digit number is such that the product of its digits is 12.When 36 is added to this number, the digits interchange their places.Find the number.

Question 9360: A two-digit number is such that the product of its digits is 12.When 36 is added to this number, the digits interchange their places.Find the number.
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
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

(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.

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