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.

Question

How many courses worth 3 credits did the student complete?

Answer 1

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.