<PRE><B>Question 257183</B>
let a = the tens digit.
let b = the ones digit.


a + b = 12 (sum of the digits is equal to 12).


10a + b = 12*a (the number is 12 times the tens digit).


solve for a in the first equation to get a = 12-b.


substitute for a in the second equation to get 10*(12-b) + b = 12*(12-b).


simplify to get:


120 - 10b + b = 144 - 12b.


combine like terms to get:


120 - 9b = 144 - 12b.


add 12b to both sides of the equation and subtract 120 from both sides of the equation to get:


3b = 24


divide both sides of the equation by 3 to get:


b = 8


if b = 8, then a = 4 because a + b = 8 + 4 = 12.


the number is 10*a + b = 40 + 8 = 48


48 is equal to 12*a = 12*4 = 48 so that part of the equation is good.


a + b = 4 + 8 = 12 so that part of the equation is also good.


your answer is the number is 48.


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