1. **State the problem:** Melanie has 75 pennies and nickels in total. The number of pennies is nine less than three times the number of nickels. We need to find how many pennies and nickels she has. 2. **Define variables:** Let $p$ be the number of pennies and $n$ be the number of nickels. 3. **Write equations based on the problem:** - Total coins: $$p + n = 75$$ - Relationship between pennies and nickels: $$p = 3n - 9$$ 4. **Substitute the second equation into the first:** $$3n - 9 + n = 75$$ 5. **Combine like terms:** $$4n - 9 = 75$$ 6. **Add 9 to both sides:** $$4n - \cancel{9} + 9 = 75 + 9$$ $$4n = 84$$ 7. **Divide both sides by 4:** $$\frac{4n}{\cancel{4}} = \frac{84}{4}$$ $$n = 21$$ 8. **Find the number of pennies using $p = 3n - 9$:** $$p = 3(21) - 9 = 63 - 9 = 54$$ 9. **Answer:** Melanie has **54 pennies** and **21 nickels**.