SOLUTION: The product of the digits of a two digit positive number is 24. If 18 is added to the number then the number is interchanged. Find the numer.

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Question 840901: The product of the digits of a two digit positive number is 24. If 18 is added to the number then the number is interchanged. Find the numer.
Answer by CubeyThePenguin(3113) About Me  (Show Source):
You can put this solution on YOUR website!
2-digit number: AB

AB = 24
10A + B + 18 = 10B + A ----> 9A - 9B = -18 ---> A - B = -2

Substitute A = B - 2 into the first equation.

(B-2)(B) = 24
B^2 - 2B - 24 = 0
(B - 6)(B + 4) = 0

The digits have to be positive, so B = 6 and A = 4.

The number is AB = 46.