SOLUTION: The sum of the digits of a 2 digit number is 9. If the digits are reversed, the number is decreased by 27. what is the original number?

Question 307067: The sum of the digits of a 2 digit number is 9. If the digits are reversed, the number is decreased by 27. 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
:
The sum of the digits of a 2 digit number is 9.
x + y = 9
y = (9-x); this form for substitution
:
If the digits are reversed, the number is decreased by 27.
10x + y = the original number
10y + x = the reversed number
:
Original number - reversed number = 27
(10x + y) - (10y + x) = 27
Remove brackets and combine like terms
10x - x - 10y + y = 27
9x - 9y = 27
Simplify, divide by 9
x - y = 3
:
Substitute (9-x) for y
x - (9-x) = 3
x + x - 9 = 3
2x = 3 + 9
2x = 12
x = 6
then
y = 9 - 6
y = 3
:
63 is the original two digit number
;
;
Check 63 - 36 = 27

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