1. **State the problem:** Vincent, Nari, and Lizbeth play a carnival game. Vincent's score is $-35$ points. Nari's score is $\frac{3}{7}$ of Vincent's score. Lizbeth scores $\frac{4}{5}$ as many points as Nari. We need to find the total points they score together. 2. **Write down the known values and formulas:** - Vincent's score: $V = -35$ - Nari's score: $N = \frac{3}{7} \times V$ - Lizbeth's score: $L = \frac{4}{5} \times N$ - Total score: $T = V + N + L$ 3. **Calculate Nari's score:** $$N = \frac{3}{7} \times (-35)$$ Simplify: $$N = \frac{3}{7} \times \cancel{-35}^{-5} = 3 \times (-5) = -15$$ 4. **Calculate Lizbeth's score:** $$L = \frac{4}{5} \times (-15)$$ Simplify: $$L = \frac{4}{5} \times \cancel{-15}^{-3} = 4 \times (-3) = -12$$ 5. **Calculate total score:** $$T = V + N + L = -35 + (-15) + (-12)$$ $$T = -35 - 15 - 12 = -62$$ **Final answer:** They score a total of $-62$ points together.