SOLUTION: When the digits of a two-digit number are reversed, the new number is 9 more than the original number, and the sum of the digits of the original number is 11. WHat is the original

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: When the digits of a two-digit number are reversed, the new number is 9 more than the original number, and the sum of the digits of the original number is 11. WHat is the original      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 183641: When the digits of a two-digit number are reversed, the new number is 9 more than the original number, and the sum of the digits of the original number is 11. WHat is the original number?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let t= the tens digit of the original number
Let u= the units digit of the original number
given:
The original number is 10t+%2B+u
The number with the digits reversed is 10u+%2B+t
(1) 10u+%2B+t+=+10t+%2B+u+%2B+9
(2) u+%2B+t+=+11
---------------------
From (1)
(1) 10u+%2B+t+=+10t+%2B+u+%2B+9
(1) 10u+-+u+%2B+t+-+10t+=+9
(1) 9u+-+9t+=+9
(1) u+-+t+=+1
Add (1) and (2)
(2) u+%2B+t+=+11
(1) u+-+t+=+1
(3) 2u+=+12
u+=+6
And, since
(2) u+%2B+t+=+11
(2) 6+%2B+t+=+11
(2) t+=+5
The original number is 56
check:
(1) 10u+%2B+t+=+10t+%2B+u+%2B+9
(1) 60+%2B+5+=+50+%2B+6+%2B+9
(1) 65+=+65
(2) u+%2B+t+=+11
(2) 6+%2B+5+=+11
(2) 11+=+11
OK