Digit-related Problems

Question

The sum of the digits of a three digit number is 15. If the tens digits and the hundreds digit are interchanged, the number is increased by 360. If the units digit is 1/4 of the sum of the hundreds and the tens digit, what is the number?

Answer 1

As mentioned in the comments, you have a system of linear equations in three variables: $$a+b+c=15\\ 100 a+10 b+c+360=10 a+100 b+c\\ c=\frac{a+b}{4} $$

Simplifying you get $$a+b+c=15\\a+4=b\\a+b=4 c$$ You can work your way from here. $$\{\{a\to 4,b\to 8,c\to 3\}\}$$