1. **State the problem:** We are given the ages of Amy, Ray, Clementine, and Jacob in the ratio 8 : 2 : 7 : 3, and their total age sum is 80 years. We need to find Clementine's age. 2. **Formula and rules:** When quantities are in ratio, we can represent each quantity as a multiple of a common variable $x$. So, Amy's age = $8x$, Ray's age = $2x$, Clementine's age = $7x$, Jacob's age = $3x$. 3. **Set up the equation:** The sum of their ages is given as 80, so: $$8x + 2x + 7x + 3x = 80$$ 4. **Simplify the equation:** $$20x = 80$$ 5. **Solve for $x$:** $$x = \frac{80}{20}$$ 6. **Show cancellation:** $$x = \frac{\cancel{80}}{\cancel{20}} = 4$$ 7. **Find Clementine's age:** Clementine's age = $7x = 7 \times 4 = 28$ **Final answer:** Clementine is 28 years old.