Amidwestern music competition awarded 38 ribbons. the number of blue ribbons awarded was 1 less than the number of white ribbons. the number of red ribbons was 3 more than the number of white ribbons. how many of each kind of ribbon was awarded?

Starting from what I know (the difference between ribbons), I decided to go from the bottom and work my way up. I then noticed a pattern (each sum was three more of the previous one), and decided to keep my pattern of the three numbers but not have to do any major mental work and instead add three to the previous sum until I got to 38.

Y=3x+1 so the first one