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. How many courses worth 3 credits did the student complete?
Let's say the student completed x courses worth 3 credits and y courses worth 4 credits.
According to the information given:
Total number of courses completed: x + y = 16 ....(1)
Total number of credits earned: 3x + 4y = 54 ....(2)
Now, we need to solve these two equations simultaneously.
Multiplying equation 1 by 3, we get:
3x + 3y = 48
Subtracting this equation from equation 2, we get:
3x + 4y - (3x + 3y) = 54 - 48
y = 6
Substitute the value of y back into equation 1:
x + 6 = 16
x = 10
Therefore, the student completed 10 courses worth 3 credits.