1. **State the problem:** We are given that 7 times as many people attended the convention on Sunday as on Thursday, and the total attendance on both days combined is 4592. We need to find the number of people who attended on Thursday and Sunday. 2. **Define variables:** Let $T$ be the number of people who attended on Thursday. Let $S$ be the number of people who attended on Sunday. 3. **Write the equations based on the problem:** $$S = 7T$$ $$T + S = 4592$$ 4. **Use substitution to solve the system:** Substitute $S = 7T$ into the second equation: $$T + 7T = 4592$$ $$8T = 4592$$ 5. **Solve for $T$:** $$T = \frac{4592}{8}$$ $$T = 574$$ 6. **Find $S$ using $S = 7T$:** $$S = 7 \times 574$$ $$S = 4018$$ 7. **Answer:** - People attended on Thursday: $574$ - People attended on Sunday: $4018$