1. **State the problem:** We have a wax candle shaped like a square base pyramid with base side length 6 inches and height 7 inches. The wax burns at a rate of 4 cubic inches every 5 hours. We need to find how many hours the candle will last. 2. **Formula for the volume of a square pyramid:** $$V = \frac{1}{3} \times \text{base area} \times \text{height}$$ where the base area for a square is side squared. 3. **Calculate the base area:** $$\text{base area} = 6 \times 6 = 36$$ 4. **Calculate the volume:** $$V = \frac{1}{3} \times 36 \times 7 = \frac{1}{3} \times 252 = 84$$ cubic inches 5. **Burn rate:** The candle burns 4 cubic inches every 5 hours, so the burn rate per hour is: $$\frac{4}{5} = 0.8$$ cubic inches per hour 6. **Calculate how long the candle lasts:** $$\text{time} = \frac{\text{total volume}}{\text{burn rate per hour}} = \frac{84}{0.8}$$ 7. **Simplify the fraction:** $$\frac{84}{0.8} = \frac{84}{\cancel{0.8}} \times \frac{\cancel{10}}{10} = \frac{840}{8}$$ 8. **Divide:** $$\frac{840}{8} = 105$$ hours **Final answer:** The candle will last **105 hours**.