SOLUTION: The sum of the digits of a two-digit number is 15. If the digits are reversed, the number is increased by 9. What is the original number?

Question 552895: The sum of the digits of a two-digit number is 15. If the digits are reversed, the number is increased by 9. What is the original number?
Found 2 solutions by KMST, mananth:
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Let x be the tens digit, and y the ones digit
The number's value is
, while the value of the number with the digits reversed is

We know that and that
--> --> -->
We solve the system

any way we can to find and
So the original number is 78.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
x+y= 15 .............1
10y+x=10x+y+9
9y=9+9x ---------2
/9 =
y=1+x
Substitute y in (1)
x+(1+x) =15
x+1+x = 15
x+x=15-1
2x = 14
/ 2
x= 7
Plug the value of x in (1)
x+y=15
1*7+ y=15
7+y=15
y=8
/ 1
y= 8
The number is 78
m.ananth@hotmail.ca

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