1. **State the problem:** The LCS Student Council bought some number of pizzas for 900 total cost. They kept 10 pizzas and sold the rest for 1040. Each pizza has 8 slices. The profit was 0.50 per slice. We need to find the total number of pizzas originally bought. 2. **Define variables:** Let $x$ = total number of pizzas originally bought. 3. **Understand the problem:** - Cost for $x$ pizzas = 900 - They kept 10 pizzas, so sold $x - 10$ pizzas - Revenue from selling $x - 10$ pizzas = 1040 - Each pizza has 8 slices, so total slices sold = $8(x - 10)$ - Profit per slice = 0.50 4. **Write the profit formula:** Profit = Revenue - Cost Given profit per slice is 0.50, total profit = $0.50 \times 8(x - 10) = 4(x - 10)$ 5. **Set up the equation:** $$\text{Profit} = \text{Revenue} - \text{Cost}$$ $$4(x - 10) = 1040 - 900$$ 6. **Simplify the right side:** $$4(x - 10) = 140$$ 7. **Divide both sides by 4:** $$x - 10 = \frac{140}{4} = 35$$ 8. **Solve for $x$:** $$x = 35 + 10 = 45$$ **Answer:** The original number of pizzas bought was $\boxed{45}$.