1. **State the problem:** Zendaya has nickels and dimes totaling 11 coins, worth 0.80 dollars. We want to find the number of nickels $x$ and dimes $y$. 2. **Set up equations:** - Total coins: $$x + y = 11$$ - Total value: $$0.05x + 0.10y = 0.80$$ 3. **Solve the system:** From the first equation, express $y$: $$y = 11 - x$$ 4. Substitute into the value equation: $$0.05x + 0.10(11 - x) = 0.80$$ 5. Distribute: $$0.05x + 1.10 - 0.10x = 0.80$$ 6. Combine like terms: $$\cancel{0.05x} - 0.10x = -0.05x$$ $$-0.05x + 1.10 = 0.80$$ 7. Subtract 1.10 from both sides: $$-0.05x = 0.80 - 1.10$$ $$-0.05x = -0.30$$ 8. Divide both sides by $-0.05$: $$x = \frac{-0.30}{-0.05} = 6$$ 9. Find $y$: $$y = 11 - 6 = 5$$ **Answer:** Zendaya has 6 nickels and 5 dimes.