Question: The soccer team is having a fundraiser and is selling cupcakes. They spent $120 on supplies and they will sell each cupcake for $2.50. The function $p(c) = 2.50c - 120$ can be used to relate the number of cupcakes sold, $c$, and the profit that is made by the club, $p(c)$, in dollars. Evaluate $p(220)$ and explain what it means in context of the problem.
1. **State the problem:** We need to evaluate the profit function $p(c) = 2.50c - 120$ when $c = 220$ cupcakes are sold.
2. **Recall the formula:** The profit function is given by $$p(c) = 2.50c - 120$$ where $2.50$ is the price per cupcake and $120$ is the fixed cost spent on supplies.
3. **Substitute $c = 220$ into the function:**
$$p(220) = 2.50 \times 220 - 120$$
4. **Calculate the multiplication:**
$$2.50 \times 220 = 550$$
5. **Calculate the profit:**
$$p(220) = 550 - 120$$
6. **Simplify the subtraction:**
$$p(220) = 430$$
7. **Interpretation:** The profit when selling $220$ cupcakes is $430$. This means the soccer team will make a profit of 430 dollars after covering the $120$ spent on supplies.