1. **State the problem:** We have a software priced at $20 each with 300 students willing to buy it. If the price increases by $5, 30 fewer students will buy it. We want to find the new price and the number of students who will buy it after the price increase. 2. **Define variables:** Let $p$ be the price of the software. Let $n$ be the number of students willing to buy it. 3. **Initial conditions:** Initial price $p_0 = 20$ Initial number of students $n_0 = 300$ 4. **Change conditions:** Price increases by $5$, so new price $p = 20 + 5 = 25$ Number of students decreases by 30, so new number of students $n = 300 - 30 = 270$ 5. **Interpretation:** After the price increase, the software costs $25$ and $270$ students are willing to buy it. 6. **Optional: Express demand as a function of price:** Assuming a linear relationship between price and number of students: $$n = m p + b$$ Using initial point $(20,300)$ and changed point $(25,270)$: Calculate slope $m$: $$m = \frac{270 - 300}{25 - 20} = \frac{-30}{5} = -6$$ Calculate intercept $b$ using point $(20,300)$: $$300 = -6 \times 20 + b \Rightarrow b = 300 + 120 = 420$$ So demand function: $$n = -6 p + 420$$ 7. **Check at new price $p=25$:** $$n = -6 \times 25 + 420 = -150 + 420 = 270$$ This matches the given data. **Final answer:** The new price is $25$ and the number of students willing to buy the software is $270$.