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 x be the number of courses worth 3 credits completed by the student.
And let y be the number of courses worth 4 credits completed by the student.
The total number of courses completed is given as x + y = 16.
The total number of credits earned is given as 3x + 4y = 54.
We can use the first equation to express y in terms of x: y = 16 - x.
Substitute y = 16 - x into the second equation: 3x + 4(16 - x) = 54.
Solve for x:
3x + 64 - 4x = 54
-x + 64 = 54
-x = -10
x = 10
Therefore, the student completed 10 courses worth 3 credits.