1. **State the problem:** We have two circles, Circle A and Circle B. - The radius of Circle A is three feet less than twice the diameter of Circle B. - The sum of the diameters of both circles is 49 feet. We need to find the area and circumference of Circle A. 2. **Define variables:** Let $d_B$ be the diameter of Circle B. Let $d_A$ be the diameter of Circle A. 3. **Translate the problem into equations:** - Radius of Circle A, $r_A = 2d_B - 3$ - Sum of diameters: $d_A + d_B = 49$ 4. **Express $d_A$ in terms of $d_B$:** Since $r_A = \frac{d_A}{2}$, we have: $$r_A = \frac{d_A}{2} = 2d_B - 3$$ Multiply both sides by 2: $$d_A = 2(2d_B - 3) = 4d_B - 6$$ 5. **Use the sum of diameters equation:** $$d_A + d_B = 49$$ Substitute $d_A$: $$4d_B - 6 + d_B = 49$$ Combine like terms: $$5d_B - 6 = 49$$ Add 6 to both sides: $$5d_B = 55$$ Divide both sides by 5: $$\cancel{5}d_B = \frac{55}{\cancel{5}}$$ $$d_B = 11$$ 6. **Find $d_A$:** $$d_A = 4d_B - 6 = 4(11) - 6 = 44 - 6 = 38$$ 7. **Find radius of Circle A:** $$r_A = \frac{d_A}{2} = \frac{38}{2} = 19$$ 8. **Calculate area of Circle A:** Formula for area: $$A = \pi r^2$$ Substitute $r_A$: $$A = \pi (19)^2 = 361\pi$$ 9. **Calculate circumference of Circle A:** Formula for circumference: $$C = 2\pi r$$ Substitute $r_A$: $$C = 2\pi (19) = 38\pi$$ **Final answers:** - Area of Circle A: $361\pi$ square feet - Circumference of Circle A: $38\pi$ feet