1. **State the problem:** Tayla bought a box of comic books for 300 and gave 15 away. She sold the rest for 330, making a profit of 1.50 on each sold comic book. We need to find the total number of comic books in the box and the original price per comic book. 2. **Define variables:** Let $x$ be the total number of comic books in the box. 3. **Write expressions:** - Number of comic books sold = $x - 15$ - Original price per comic book = $\frac{300}{x}$ - Selling price per comic book = original price + 1.50 = $\frac{300}{x} + 1.50$ 4. **Set up equation for total selling price:** $$330 = (x - 15) \times \left(\frac{300}{x} + 1.50\right)$$ 5. **Expand and simplify:** $$330 = (x - 15) \times \frac{300}{x} + (x - 15) \times 1.50$$ $$330 = \frac{300(x - 15)}{x} + 1.50x - 22.5$$ 6. **Multiply both sides by $x$ to clear denominator:** $$330x = 300(x - 15) + (1.50x - 22.5)x$$ $$330x = 300x - 4500 + 1.50x^2 - 22.5x$$ 7. **Bring all terms to one side:** $$0 = 300x - 4500 + 1.50x^2 - 22.5x - 330x$$ $$0 = 1.50x^2 + (300 - 22.5 - 330)x - 4500$$ $$0 = 1.50x^2 - 52.5x - 4500$$ 8. **Divide entire equation by 1.5 to simplify:** $$0 = \cancel{1.50}x^2 - \cancel{1.50}35x - \cancel{1.50}3000$$ $$0 = x^2 - 35x - 3000$$ 9. **Solve quadratic equation:** $$x = \frac{35 \pm \sqrt{35^2 + 4 \times 3000}}{2} = \frac{35 \pm \sqrt{1225 + 12000}}{2} = \frac{35 \pm \sqrt{13225}}{2}$$ $$\sqrt{13225} = 115$$ 10. **Calculate roots:** $$x = \frac{35 + 115}{2} = 75 \quad \text{or} \quad x = \frac{35 - 115}{2} = -40$$ 11. **Interpret solution:** Number of comic books cannot be negative, so $x = 75$. 12. **Find original price per comic book:** $$\frac{300}{75} = 4$$ **Final answers:** - Total comic books in the box: 75 - Original price per comic book: 4