Answer: 275
Step-by-step explanation:
Let x represent the hundred digit
Let y represent the tens digit
Let z represent the unit digit
The sum of the digits in a three-digit number is 14. This means that
x + y + z = 14
The sum of the hundreds digit and the units digit is equal to the tens digit. This means that
x + z = y
If the hundreds digit and the units digit are interchanged, the new digit would be x + 10y + 100z. If the number is increased by 297, then
x + 10y + 100z = 100x + 10y + z + 297
x - 100x + 10y - 10y + 100z - z = 297
- 99x + 99z = 297
Substituting y = x + z into the first equation, we have
x + x + z + z = 14
2x + 2z = 14
Dividing through by 2,
x + z = 7
Substituting x = 7 - z into - 99x + 99z = 297, we have
- 99(7 - z) + 99z = 297
- 693 + 99z + 99z = 297
99z + 99z = 297 + 693
198z = 990
Dividing both sides by 198, we have
z = 990/198
z = 5
x = 7 - z = 7 - 5
x = 2
y = x + z = 2 + 5
y = 7
Thus, the original number is
275