It’s less than 300

Question

The ones digit 4 times the hundred digit
The tens digit is 5 more than the hundreds digit
The sum of the digits is 17

Answer 1

Let hundreds digit = x

The tens digit is 5 more than the hundreds digit means:

tens digit = x + 5

The ones digit 4 times the hundred digit means:

ones digit = 4 x

The sum of the digits is 17 means:

hundreds digit + tens digit + ones digit = 17

x + x + 5 + 4 x = 17

6 x + 5 = 17

Subtract 5 to both sides

6 x = 12

x = 12 / 6 = 2

hundreds digit = x = 2

tens digit = x + 5 = 2 + 5 = 7

ones digit = 4 x = 4 ∙ 2 = 8

Your number is:

278

Answer 2

The number starts with a 1 or 2, so it has the form
1?4 or 2?8
Since the digits sum to 17, and the maximum digit is 9, 1?4 is out
That just leaves 278