A college student completed some courses worth 3 credits and some courses worth 4 credits. The student earned a total of 54 credits after completing a total of 16 courses.%0D%0A%0D%0A%0D%0A%0D%0AHow 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.
We know that x + y = 16 (total number of courses completed) and 3x + 4y = 54 (total number of credits earned).
Solving the system of equations:
x + y = 16
3x + 4y = 54
Multiplying the first equation by 4, we get:
4x + 4y = 64
Subtracting this equation from the second equation:
3x + 4y - 4x - 4y = 54 - 64
-x = -10
x = 10
Plugging x back into the first equation:
10 + y = 16
y = 6
So, the student completed 10 courses worth 3 credits.