1. **State the problem:** Dakola purchased tickets costing 35.50 each plus a 7 handling charge, spending less than 150 in total. We need to find the greatest number of tickets she could buy. 2. **Write the inequality:** Let $x$ be the number of tickets. The total cost is $7 + 35.50x$. Since she spent less than 150, the inequality is: $$7 + 35.50x < 150$$ 3. **Solve the inequality:** Subtract 7 from both sides: $$\cancel{7} + 35.50x - \cancel{7} < 150 - 7$$ $$35.50x < 143$$ 4. Divide both sides by 35.50: $$\frac{35.50x}{35.50} < \frac{143}{35.50}$$ $$x < 4.028169014$$ 5. Since $x$ represents the number of tickets, it must be a whole number less than 4.028, so the greatest integer $x$ is 4. **Final answer:** Dakola can purchase at most **4 tickets**.