digits of positive number

Question

The sum of the two digits of a positive integer is 12.  When the digits were reversed, the new number was 54 greater than the original.  What is the product of the digits of the original number minus the original number?

Answer 1

a + b = 12

10b + a = 10a + b + 54

 

a = 12 - b

10b + (12 - b) = 10(12 - b) + b + 54

 

Solve for b, take the solution and plug it into the first equation to solve for a, then use your two digits for the rest. You got this!