how many numbers have this property: when you subtract 297 from it, you get the same number but in reverse.

9514 1404 393

  60

Step-by-step explanation:

Consider the number with digits x, y, z. Its value will be 100z+10y+z. We want the same value when we reverse the digits after subtracting 297.

  100x +10y +z -297 = 100z +10y +x

  99x -99z = 297 . . . . . subtract 100z+10y+x-297

  x -z = 3 . . . . . . . . . . . . divide by 99

The first digit of the number is 3 more than the last digit. There are 60 such numbers. The first digit may be 4..9, and the middle digit may be 0..9.

  401, 502, 603, ..., 906; 411, 512, 613, ..., 916, ..., 491, 592, 693, ... 996