A state college has separate fee retes for resident students and nonresident students. Resident students are charged `$412` per semester and nonresident students are charged `$879` per semester. The college's sophomore class of 1,980 students paid a total of `$1,170,210` in fees for the most recent semester. Which of the following systems of equations represents the number of resident (r) and nonresident (n) sophomores and the amount of fees the two groups paid ?

Options

A. `r +n =1,170, 210`
`421r +879n =1,980`
B. `r +n =1,980`
`879r +421n=1,170, 210`
C. `r +n=1,980`
`421r +879n = 1,170, 210`
D. `r +n=1,170, 210`
`879r +421n =1,980`

Explanation

To solve the problem, we need to set up a system of equations based on the information provided about resident and non-resident students at the college.

### Step-by-Step Solution:

1. **Define Variables**:
- Let \( r \) be the number of resident students.
- Let \( n \) be the number of non-resident students.

2. **Set Up the First Equation**:
- The total number of students is given as 1,980. Therefore, we can write the first equation as:
\[ r + n = 1980 \]

3. **Set Up the Second Equation**:
- The fees charged to resident students is $412 per semester, and for non-resident students, it is $879 per semester. The total fees collected from all students is $1,170,210. Thus, the second equation can be expressed as:
\[ 412r + 879n = 1170210 \]

4. **Write the System of Equations**:
- Combining both equations, we have the following system:
\[ \begin{cases} r + n = 1980 \\ 412r + 879n = 1170210 \end{cases} \]

5. **Conclusion**:
- The system of equations that represents the number of resident and non-resident sophomores and the amount of fees paid by the two groups is:
\[ \begin{cases} r + n = 1980 \\ 412r + 879n = 1170210 \end{cases} \]