Question

The number xy is such that three times the sum of it's digits is less than the value of the number by 8. When the digits are reversed the value of the number increases by 9.find the number

Answer 1

3(x+y) = 10x+y - 8
10y+x = 10x+y + 9
so now just solve as usual.

Answer 2

3(x+y) + 8 = 10 x + y
10 y + x = 9 + 10 x + y

3 x + 3 y = 10 x + y - 8
9 y - 9 x = 9

- 7 x + 2 y = -8
-9 x + 9 y = 9

-63 x + 18 y = -72
-18 x + 18 y = 18
--------------------------- subtract
-45 x +0 = -90
x = 2
-7 (2) + 2 y = -8
-14 + 2y = -8
2 y = 6
y = 3
so at last
23