1. **State the problem:** We want to find the profit function $P(x)$ where $x$ is the additional amount charged per seat above $5$ dollars. 2. **Define variables:** - Base price per seat: $5$ - Additional charge: $x$ - Total price per seat: $5 + x$ - Base attendance: $555$ fans - Attendance decreases by $30$ fans for each additional dollar charged, so attendance is $555 - 30x$ 3. **Write the profit function:** Profit $P(x)$ is price per seat times attendance: $$P(x) = (5 + x)(555 - 30x)$$ 4. **Expand the expression:** $$P(x) = 5 \times 555 - 5 \times 30x + x \times 555 - 30x^2$$ $$P(x) = 2775 - 150x + 555x - 30x^2$$ 5. **Combine like terms:** $$P(x) = 2775 + 405x - 30x^2$$ 6. **Rewrite in standard quadratic form:** $$P(x) = -30x^2 + 405x + 2775$$ 7. **Interpretation:** This matches option B. **Final answer:** $$P(x) = -30x^2 + 405x + 2775$$