SOLUTION: The sum of the digits of a two digit counting number is 15 , when the digits are reversed the number is 27 more than the original number . what was the original number?

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Question 1150396: The sum of the digits of a two digit counting number is 15 , when the digits are reversed the number is 27 more than the original number . what was the original number?
Found 2 solutions by ikleyn, Alan3354:
Answer by ikleyn(52780)   (Show Source): You can put this solution on YOUR website!
. 

Let "a" be the tens digit of the 2-digit number, and

let "b" be the ones digit of the number.


Then the number is

    n = 10a + b,         (1)


while the reversed digit number is 

    m = 10b + a.         (2)


The sum of the digits "a" and "b" is 15

    a + b = 15.          (3)


According to the condition, the reversed number is 27 more than the original number.  It means


    (10b+a) - (10a+b) = 27,    or

    9b - 9a = 27,

    9*(b-a) = 27,

    b-a     = 27/9 = 3.    (4)


Thus we have the system of two equations

    b + a = 15             (3')

    b - a =  3             (4')


To solve it, from equation (3') express a = 15-b  and express it into equation (4').  You will get then

    b - (15-b) = 3

    2b = 3+15 = 18,

    b = 18/2 = 9.


Then from equation (1'),  a = 15-9 = 6.


Thus the number is  69.


CHECK.  The reversed number MINUS the original number is  96 - 69 = 27.   ! Correct !

Solved.


Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
The sum of the digits of a two digit counting number is 15, when the digits are reversed the number is 27 more than the original number . what was the original number?
------------------
Reversing the digits of a 2 digit integer changes the value by 9 times the difference between the digits.
================
T + U = 15
T - U = 3
---------------- Add
2T = 18
T = 9
U = 6
--------
Since reversing increases the value, the Tens is the smaller number.
---> 69
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