A university student completed courses worth 3 credits and some courses worth 4 credits. The student earned a total of 54 credits after completing 15 courses. How many courses worth 4 credits did the student complete?
Let X be the number of courses worth 4 credits.
The student completed 15 – X courses worth 3 credits.
The total number of credits from courses worth 4 credits is X * 4 = 4X.
The total number of credits from courses worth 3 credits is (15 – X) * 3 = 45 – 3X.
The total number of credits earned is 4X + 45 – 3X = 54.
Combining like terms, we get X – 45 = 54 – 54
Combining like terms, we get X – 45 = 0
Adding 45 to both sides, we get X = 45.
The student completed 45 / 4 = <<45/4=11.25>>11.25 courses worth 4 credits.
The student completed 15 – 11.25 = <<15-11.25=3.75>>3.75 courses worth 3 credits.
Since they cannot have 0.25 of a course, the student completed 11 courses worth 4 credits. Answer: \boxed{11}.