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?
3
10
21
38
Let's say the student completed x courses worth 3 credits and y courses worth 4 credits. We know that the total number of courses completed is 16, so x + y = 16.
We also know that the total number of credits earned is 54, so 3x + 4y = 54.
Now we can solve these two equations simultaneously.
From the first equation, we can write y = 16 - x.
Substitute this into the second equation:
3x + 4(16 - x) = 54
3x + 64 - 4x = 54
-x + 64 = 54
-x = 54 - 64
-x = -10
x = 10
So, the student completed 10 courses worth 3 credits.
Therefore, the answer is 10.