SOLUTION: The sum of the digits of a two-digit number is 9. If the digits are reversed, the number is 27 less than the original. Find the original number.

Question 179803: The sum of the digits of a two-digit number is 9. If the digits are reversed, the number is 27 less than the original. Find the original number.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The sum of the digits of a two-digit number is 9. If the digits are reversed,
the number is 27 less than the original. Find the original number.
:
Let x = the 10's digit
Let y = the units digit
then
10x + y = the two-digit number
:
"The sum of the digits of a two-digit number is 9."
x + y = 9
y = (9-x)
:
"If the digits are reversed, the number is 27 less than the original."
10y + x = (10x + y) - 27
10y - y = 10x - x - 27
9y = 9x - 27
Simplify, divide by 9
y = x - 3
Substitute (9-x) for y
9 -x = x - 3
9 + 3 = x + x
12 = 2x
x = 6, then obviously y = 3
;
63 is the original number
:
Check solution in the statement:
"If the digits are reversed, the number is 27 less than the original."
36 = 63 - 27

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