(Sorry, not sure how much detail you want so providing a lot in the steps.)

Consider A is a side of the small square and B is the side of the large square.

Since the large square has sides three inches longer than the small square, we know that B=A+3.

We also know the area of a square with side s is s^2. Thus the large square's area is B^2 and the small square's area is A^2.

If the sum of the small square's and the large square's areas are 485, we can conclude 

A^2+B^2=485 and by extension A^2+(A+3)^2=485.

From there we can extend the equation to A^2+(A^2+6A+9)=485 which simplifies to 2A^2+6A=476 by adding like terms.

Divide the whole equation by 2 to end up with A^2+3A=238 and if you move the 238 to the other side, you end up with A^2+3A-238=0

When you factor the equation, you obtain (A-14)(A+17) (because -14+17=3 and -14*17=-238) giving you two possible values A=14 and A=-17. Since the length of a square cannot be negative, A must be 14.

We plug 14 into our B equation, so B=14+3. Thus B is 17.