1. **State the problem:** Zach paid 8 for an 8-inch diameter pizza, and Aiden paid 12 for a 12-inch diameter pizza. We need to find the percentage increase in price and size, then determine who got the better deal. 2. **Formulas and rules:** - Percentage increase formula: $$\text{Percentage Increase} = \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100\%$$ - Pizza size is proportional to the area of the circle: $$\text{Area} = \pi \times \left(\frac{\text{diameter}}{2}\right)^2$$ 3. **Calculate percentage increase in price:** $$\text{Price Increase} = \frac{12 - 8}{8} \times 100\% = \frac{4}{8} \times 100\% = 50\%$$ 4. **Calculate areas of pizzas:** - Zach's pizza area: $$\pi \times \left(\frac{8}{2}\right)^2 = \pi \times 4^2 = 16\pi$$ - Aiden's pizza area: $$\pi \times \left(\frac{12}{2}\right)^2 = \pi \times 6^2 = 36\pi$$ 5. **Calculate percentage increase in size:** $$\text{Size Increase} = \frac{36\pi - 16\pi}{16\pi} \times 100\% = \frac{20\pi}{16\pi} \times 100\% = \frac{20}{16} \times 100\% = 125\%$$ 6. **Compare deals:** - Price increased by 50%, but size increased by 125%. - Aiden paid more, but got a much larger pizza. - Therefore, Aiden got the better deal because the size increase percentage is greater than the price increase percentage. **Final answer:** - Percentage increase in price: 50%. - Percentage increase in size: 125%. - Aiden got the better deal.