Algebra Question: I believe two equations and two unknowns

Question

On a field trip, the students are assigned exactly 7 students per room.  To save money the next day, the school decided to return two rooms, but they were still able to assign 8 students exactly to each room.  How many students are on the trip?

Answer 1

S = the number of students.  This remains the same for both days.

R = the number of rooms on the first day.

The number of rooms on the second day would be R-2.

First day:

S = 7R

Second Day:

S = 8(R-2)

Since S is the same for both days,

8(R-2) = 7R

8R-16 = 7R

R = 16

Use the either day's equation to find S.  The first day's looks simpler:

S = 7R

S = (7)(16)

S = 112