Question

A college student completed some courses worth 6 credits and some courses worth 4 credits. The student earned a total of 104 credits after completing 21 courses.How many courses worth 4 credits did the student complete?A. 11B. 26C. 13 D. 10

Answer 1

Let x be the number of four credit courses and let y be the number of six credit courses.

We know that the student have completed 21 courses, this means that:

$x+y=21$

We also know that he has 104 credits in total. This means that:

$4x+6y=104$

Then we have the system of equations:

$\begin{gathered} x+y=21 \\ 4x+6y=104 \end{gathered}$

To solve the system we solve the first equation for y and plug the value in the second one. That is:

$y=21-x$$\begin{gathered} 4x+6(21-x)=104 \\ 4x+126-6x=104 \\ -2x=104-126 \\ -2x=-22 \\ x=\frac{-22}{-2} \\ x=11 \end{gathered}$

Therefore, the student has taken 11 four credit courses.