SOLUTION: The sum of the digits of a 2-digit number is 8. When 36 is added to the number, the digits are reversed. What would be the number?

Question 235355: The sum of the digits of a 2-digit number is 8. When 36 is added to the number, the digits are reversed. What would be the 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
:
10x + y = the two digit number
:
The sum of the digits of a 2-digit number is 8.
x + y = 8
y = (8-x)
:
When 36 is added to the number, the digits are reversed.
10x + y + 36 = 10y + x
10x - x = 10y - y - 36
9x = 9y - 36
Simplify, divide by 9:
x = y - 4
:
What would be the number?
replace y with (8-x)
x = (8-x) - 4
x + x = 8 -4
2x = 4
x = 2
then
y = 8 - x
y = 8 - 2
y = 6
:
26 is the number
:
:
Check solution
26 + 36 = 62
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