Question

A college has separate fee rates for US students and non-US students. US students are charged $\$421$ per semester while non-US 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 represents the number of US student $\left(r\right)$ and non-US $\left(n\right)$ sophomores and the amount of fees the two groups paid?

• 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. $r+n=1,170,210$
  $879r+421n=1,980$

Answer 1

The correct option is C $r+n=1,980$

$421r+879n=1,170,210$
Given in question in the college number of US students $\left(r\right)$ and number of non US students $\left(n\right)$

Then, total students = $r+n$

But fee paid by 1$980$ students

Then $r+n=1980$.............................................(1)

And fee rates charged by US students 421$persemesterand$ $879$ for non US students and total fee collected 1,170,210$ for recent semester

Then, fee paid by US students$=421r$

And fee paid by non US students $=879n$

But, the total fee paid by group of students $1,170,210$

So, $421r+879n=1,170,210.$.......................................(2)