A university student completed courses worth 3 credits and some courses worth 4 credits. The student earned a total of 54 credits after completing 16 courses. How many courses worth 3 credits did the student complete?
Let x be the number of courses worth 3 credits and y be the number of courses worth 4 credits.
According to the given information, the total number of courses completed is 16:
x + y = 16
Also, the total number of credits earned is 54:
3x + 4y = 54
Now we can solve these two equations simultaneously to find the values of x and y.
From the first equation:
x = 16 - y
Substitute this into the second equation:
3(16 - y) + 4y = 54
48 - 3y + 4y = 54
y = 6
So, the student completed 6 courses worth 4 credits. Now we can find the number of courses worth 3 credits by substituting y = 6 back into the first equation:
x + 6 = 16
x = 10
Therefore, the student completed 10 courses worth 3 credits.