1. **State the problem:** We have a ticket sale where students pay 2 each and faculty pay 4 each. A total of 120 tickets were sold and total revenue was 380. 2. **Define variables:** Let $S$ = number of students, $F$ = number of faculty. 3. **Write system of equations:** Total tickets: $$S + F = 120$$ Total revenue: $$2S + 4F = 380$$ 4. **Solve the system:** From the first equation: $$S = 120 - F$$ Substitute into the second: $$2(120 - F) + 4F = 380$$ $$240 - 2F + 4F = 380$$ $$240 + 2F = 380$$ Subtract 240 from both sides: $$2F = 380 - 240$$ $$2F = 140$$ Divide both sides by 2: $$F = \cancel{\frac{2F}{2}}{=} \frac{140}{2} = 70$$ 5. **Find $S$:** $$S = 120 - F = 120 - 70 = 50$$ 6. **Answer:** There were 50 students and 70 faculty who bought tickets.