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 wor
th 3 credits did the student complete?
Let's denote the number of courses worth 3 credits as x, and the number of courses worth 4 credits as y.
Given:
x + y = 16 (total number of courses)
3x + 4y = 54 (total number of credits earned)
Now, we can solve these equations simultaneously to find the values of x and y.
From the first equation:
x = 16 - y
Substitute this expression for x into the second equation:
3(16 - y) + 4y = 54
48 - 3y + 4y = 54
48 + y = 54
y = 54 - 48
y = 6
Now, substitute the value of y back into the equation x = 16 - y:
x = 16 - 6
x = 10
Therefore, the student completed 10 courses worth 3 credits and 6 courses worth 4 credits.