Question 1133718
A number consist of 3 digits whose sum is 14,
a + b + c = 14
 the middle digit is equal to the sum of the other two.
b = a + c
 If you reverse its digit the original number will be lesser by 99.
100a + 10b + c + 99 = 100c + 10b + a
100a - a + 10b - 10b + 99 = 100c - c
99a + 99 = 99c
simplify, divide by 99
a + 1 = c
:
We got 3 simple equation and 3 unknowns so this should be easy
in the 2nd equation, replace c with a+1
b = a + (a+1)
b = 2a + 1
:
in the first equation replace b with (2a+1); replace c with (a+1)
a + (2a+1) + (a+1) = 14
4a + 2 = 14
4a = 14 - 2
4a = 12
a = 3
then
b = 2(3) + 1
b = 7
and
c = 3 + 1
c = 4
:
Check 3 + 7 + 4 = 14 and 374 + 99 = 473

 Find the number. 374