1. **State the problem:** We have two types of coins: $5 coins and 20¢ coins. The total number of coins is 20, and the total value is 37.6 (dollars). We need to find the number of each type of coin. 2. **Define variables:** Let $x$ be the number of $5 coins and $y$ be the number of 20¢ coins. 3. **Write equations based on the problem:** - Total coins: $$x + y = 20$$ - Total value: $$5x + 0.20y = 37.6$$ 4. **Solve the system of equations:** From the first equation, express $y$ in terms of $x$: $$y = 20 - x$$ Substitute into the second equation: $$5x + 0.20(20 - x) = 37.6$$ 5. **Simplify and solve for $x$:** $$5x + 4 - 0.20x = 37.6$$ $$5x - 0.20x = 37.6 - 4$$ $$4.8x = 33.6$$ Divide both sides by 4.8: $$\frac{\cancel{4.8}x}{\cancel{4.8}} = \frac{33.6}{4.8}$$ $$x = 7$$ 6. **Find $y$:** $$y = 20 - 7 = 13$$ 7. **Answer:** There are 7 coins of $5 and 13 coins of 20¢.