SOLUTION: the sum of the digits of a two-digit number is 17. When the digits are reversed, the new number is 9 more than the original number. What is the original number?

Question 397250: the sum of the digits of a two-digit number is 17. When the digits are reversed, the new number is 9 more than the original number. What is the original number?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
let x = the 10's digit
let y = the units
then
10x + y = the original two digit number
and
10y + x = the two digit number reversed
:
the sum of the digits of a two-digit number is 17.
x + y = 17
:
When the digits are reversed, the new number is 9 more than the original number.
10y + x = 10x + y + 9
10y - y = 10x - x + 9
9y = 9x + 9
simplify, divide by 9
y = x + 1
:
Replace y with (x+1) in the 1st equation
x + x+1 = 17
2x = 17-1
2x = 16
x = 8
then, obviously, y = 9
:
What is the original number? 89
:
:
Confirm this in the statement:
"When the digits are reversed, the new number is 9 more than the original"
98 = 89 + 9
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