Final answer:
Miranda's age is 14 and Bailey's age is 15. The sum of their ages is 29.
Step-by-step explanation:
To find the sum of their ages, we need to find their ages. Let's assume that Miranda's age is x and Bailey's age is x+1. We are given that the product of their ages is 210, so we can write the equation x(x+1) = 210. Expanding the equation, we have x^2 + x - 210 = 0. We can solve this quadratic equation by factoring or using the quadratic formula. Factoring, we have (x + 15)(x - 14) = 0. This gives us two possible solutions: x = -15 or x = 14. Since age cannot be negative, we can disregard x = -15. Therefore, Miranda's age is 14 and Bailey's age is 15. To find the sum of their ages, we add their ages together: 14 + 15 = 29. So, the sum of Miranda and Bailey's ages is 29.