1. **State the problem:** We need to find the number of 1-peso coins and 25-centavo coins that total 20 coins and amount to 9.50 pesos. 2. **Define variables:** Let $x$ be the number of 1-peso coins. Let $y$ be the number of 25-centavo coins. 3. **Write the system of equations:** - Total coins: $$x + y = 20$$ - Total amount: $$1 \cdot x + 0.25 \cdot y = 9.50$$ 4. **Solve the system:** From the first equation, express $y$ as: $$y = 20 - x$$ Substitute into the second equation: $$x + 0.25(20 - x) = 9.50$$ Simplify: $$x + 5 - 0.25x = 9.50$$ $$0.75x + 5 = 9.50$$ Subtract 5 from both sides: $$0.75x = 4.50$$ Divide both sides by 0.75: $$x = \frac{4.50}{0.75} = 6$$ 5. **Find $y$:** $$y = 20 - 6 = 14$$ 6. **Verify the solution:** Total amount: $$6 \times 1 + 14 \times 0.25 = 6 + 3.50 = 9.50$$ Total coins: $$6 + 14 = 20$$ **Answer:** Allysa has 6 one-peso coins and 14 twenty-five centavo coins.