1. **State the problem:** Callie's company has fixed monthly expenses of $3200 and variable costs of $2.40 per pillow. Each pillow sells for $18. We want to find the number of pillows $p$ that must be sold to make a profit. 2. **Define profit:** Profit = Total Revenue - Total Cost 3. **Write expressions for revenue and cost:** - Revenue from selling $p$ pillows: $$18p$$ - Cost includes fixed expenses plus variable cost per pillow: $$3200 + 2.40p$$ 4. **Set up inequality for profit:** Profit > 0 means $$18p - (3200 + 2.40p) > 0$$ 5. **Simplify the inequality:** $$18p - 3200 - 2.40p > 0$$ $$ (18 - 2.40)p - 3200 > 0$$ $$15.6p - 3200 > 0$$ 6. **Isolate $p$:** $$15.6p > 3200$$ Divide both sides by 15.6: $$\cancel{15.6}p > \cancel{15.6} \frac{3200}{15.6}$$ $$p > \frac{3200}{15.6}$$ 7. **Calculate the value:** $$p > 205.1282...$$ 8. **Interpretation:** Since $p$ must be a whole number of pillows, the company must sell at least 206 pillows to make a profit. **Final answer:** $$\boxed{206}$$ pillows must be sold to make a profit.