1. **State the problem:** We are given a profit function $p$ that depends on the number of students $n$ attending a dance. The profit is calculated as 4 times the number of students minus 200 dollars for music costs. 2. **Write the formula:** The profit function is $$p = 4n - 200$$ where $p$ is the profit and $n$ is the number of students. 3. **Explain the formula:** For every student attending, the profit increases by 4 dollars. However, there is a fixed cost of 200 dollars that must be subtracted from the total. 4. **Calculate some values:** - If $n=0$, then $p = 4(0) - 200 = -200$ (a loss of 200 dollars). - If $n=50$, then $p = 4(50) - 200 = 200 - 200 = 0$ (break-even point). - If $n=100$, then $p = 4(100) - 200 = 400 - 200 = 200$ (a profit of 200 dollars). 5. **Interpretation:** The profit increases linearly with the number of students. The break-even point is when $p=0$, which happens at $n=50$ students. 6. **Graphing:** The graph of $p = 4n - 200$ is a straight line with slope 4 and y-intercept -200. **Final answer:** The profit function is $$p = 4n - 200$$ and the break-even number of students is 50.