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?

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) (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
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