1. Let's define the variables: Let $r$ be Rachel's age. 2. Monica is a year older than Rachel, so Monica's age is $r + 1$. 3. According to the problem, multiplying their ages and adding Monica's age gives 25: $$r \times (r + 1) + (r + 1) = 25$$ 4. Simplify the equation: $$r(r + 1) + r + 1 = 25$$ $$r^2 + r + r + 1 = 25$$ $$r^2 + 2r + 1 = 25$$ 5. Subtract 25 from both sides to set the equation to zero: $$r^2 + 2r + 1 - 25 = 0$$ $$r^2 + 2r - 24 = 0$$ 6. Factor the quadratic equation: $$(r + 6)(r - 4) = 0$$ 7. Solve for $r$: $$r + 6 = 0 \Rightarrow r = -6$$ $$r - 4 = 0 \Rightarrow r = 4$$ 8. Since age cannot be negative, Rachel's age is $4$. Final answer: Rachel is 4 years old.