1. **State the problem:** You have 25 coins total, all nickels and quarters, with a total value of 3.85. Find the number of nickels $n$ and quarters $q$. 2. **Write the equations:** - Total coins: $n + q = 25$ - Total value: $0.05n + 0.25q = 3.85$ 3. **Convert value equation to cents to avoid decimals:** $5n + 25q = 385$ 4. **Simplify the value equation by dividing all terms by 5:** $$\cancel{5}n + \cancel{25}q = \cancel{385}$$ becomes $n + 5q = 77$ 5. **Now solve the system:** From the first equation: $n = 25 - q$ Substitute into the second: $25 - q + 5q = 77$ Simplify: $25 + 4q = 77$ 6. **Isolate $q$:** $4q = 77 - 25$ $4q = 52$ Divide both sides by 4: $$\cancel{4}q = \cancel{52}$$ $q = 13$ 7. **Find $n$:** $n = 25 - 13 = 12$ **Answer:** There are 12 nickels and 13 quarters.