Question

Find a three-digit positive integers such that the sum of all three digit is i4, the tens digit is two more than ones and if the digit is reversed, the number is unchanged.

Answer 1

let the unit be be x
then the tens digit is x+2
let the hundreds digit by y

x + x+2 + y = 14
2x + y = 12

number: 100y + 10(x+2) + x
= 100y + 11x + 20

number reversed:
100x + 10(x+2) + y
= 110x + y + 20

but they are to be equal
100y + 11x + 20 = 110x + y + 20
99y = 99x
y = x
back into 2x+y = 12
2x+x=12
x = 4, then y = 4

the number is 454