SOLUTION: The sum of the digits of a two-digit number is 15. If the digits are reversed, the new number is 27 less than the original number. Find the original number.

Algebra ->  Systems-of-equations -> SOLUTION: The sum of the digits of a two-digit number is 15. If the digits are reversed, the new number is 27 less than the original number. Find the original number.      Log On


   

Question 30291: The sum of the digits of a two-digit number is 15. If the digits are reversed, the new number is 27 less than the original number. Find the original number.
Found 2 solutions by Paul, smoothflyin:
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
THe original number is 10x+y
x is the ten digit and y is the one digit
Sum:
x+y=15
y=15-x (subsitution)


Digits reversed:
10y+x --. Now the ones is tens and the tens is ones:
10y+x=(10x+y)-27
10(15-x)+x=10x+15-x-27
150-9x=9x-12
-18x=-162
x=9

y=15-9
y=6

Hence, the 2 digit number is 96. 9-->10 digit and 6-->one digit.
Paul.

Answer by smoothflyin(6) About Me  (Show Source):
You can put this solution on YOUR website!
The numbers are 9 and 6
96 - 69 = 27