SOLUTION: The sum of the digits of a two-digit number is 12. The number formed by interchanging the digits is 54 more than the orginal number. find the original number and its reversal.

Algebra ->  Equations -> SOLUTION: The sum of the digits of a two-digit number is 12. The number formed by interchanging the digits is 54 more than the orginal number. find the original number and its reversal.       Log On


   

Question 147014: The sum of the digits of a two-digit number is 12. The number formed by interchanging the digits is 54 more than the orginal number. find the original number and its reversal.

thank you
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let the first digit in the original number be A.
Let the second digit in the original number be B.
1.A%2BB=12
The number can be represented as
10%2AA%2BB
The number with digits transposed would be
10%2AB%2BA
Putting all those together would yield,
10%2AB%2BA=10%2AA%2BB%2B54
-9A%2B9B=54
2.-A%2BB=6
Add eq.1 and eq.2 and solve for B.
A%2BB-A%2BB=12%2B6
2B=18
B=9
From 1,
A%2BB=12
A%2B9=12
A=3
Original number is 39.
Transposed number is 93.