A local retailer has determined that the number $x$ of PortaBoy game systems sold in a week is related to the price $p$ in dollars of each system. 70 game systems were sold when the price was $40. When the systems went on sale the following week, 175 systems were sold at $25 a piece.
(a) Find a linear function which fits this data. Use the weekly sales $x$ as the independent variable and the price $p$ as the dependent variable.
Answer: $p(x) = -\frac{1}{7}x + 50$
(b) Find a suitable applied domain: $x > 0$
(c) If the retailer wants to sell 245 PortaBoys next week, what should the price be?
Answer: $p = 15$ dollars