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t = the tens digit
u = the units (ones) digit
10t+u = the number
10u+t = the number reversed
The sum of the two digits of a two-digit number is 6.
t + u = 6
When 18 is added to the number the digits are reversed.
10t+u + 18 = 10u+t
10t + u + 18 = 10u + t
-10u -10u
-----------------------
10t - 9u + 18 = t
-t -t
-----------------------
9t - 9u + 18 = 0
- 18 -18
-----------------------
9t - 9u = -18
9t - 9u = -18
Divide every term by 9
t - u = -2
Add the two equations:
2t = 4
t = 2
Substitute in t+u = 6
2+u = 6
-2 -2
--------
u = 4
The number is 24
Checking:
24
+18
---
42
24 is the number and when we add 18
we get its reverse, which is 42.
Edwin
