Let the radii of the two circles be r1 and r2. The sum of the areas of the two circles is given as 153 π sq cm. The area of a circle with radius r is πr². So, πr1² + πr2² = 153 π. Dividing by π, we get r1² + r2² = 153. The sum of their radii is given as 15 cm. So, r1 + r2 = 15. We have a system of equations: 1) r1² + r2² = 153 2) r1 + r2 = 15 From (2), r2 = 15 - r1. Substitute this into (1): r1² + (15 - r1)² = 153 r1² + 225 - 30r1 + r1² = 153 2r1² - 30r1 + 225 - 153 = 0 2r1² - 30r1 + 72 = 0 Dividing by 2: r1² - 15r1 + 36 = 0 This is a quadratic equation. Factoring (finding two numbers that multiply to 36 and add to -15) gives (r1 - 3)(r1 - 12) = 0. So, the possible values for r1 are 3 or 12. If r1 = 3, then r2 = 15 - 3 = 12. If r1 = 12, then r2 = 15 - 12 = 3. The radii are 3 cm and 12 cm. The larger radius is 12 cm and the smaller radius is 3 cm. The ratio of the larger to smaller radius is 12 : 3, which simplifies to 4 : 1.