SOLUTION: The sum of the digits of a two-digit number is 14. When the digits are reversed, the new number is 36 more than the original number. What is the original number?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: The sum of the digits of a two-digit number is 14. When the digits are reversed, the new number is 36 more than the original number. What is the original number?       Log On


   

Question 532455: The sum of the digits of a two-digit number is 14. When the digits are reversed, the new number is 36 more than the original number. What is the original number?
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the digits of a two-digit number is 14. When the digits are reversed, the new number is 36 more than the original number. What is the original number?
**
let x=one's digit
let t=ten's digit
x+t=14 (eq 1)
x=14-t
..
original number=x+10t
reversed new number=10x+t
reversed new number-original number=36
10x+t-x-10t=36
9x-9t=36 (eq 2)
x+t=14 (eq 1)
multiply (eq 1) by 9
9x+9t=126 (eq 3)
add (eq 2) and (eq 3)
18x=162
x=9
t=14-x=5
ans:
original number=59
new number=95