1. **State the problem:** Maria has only nickels and dimes, totaling 20 coins, worth 165 cents. Find the number of dimes. 2. **Define variables:** Let $n$ = number of nickels, $d$ = number of dimes. 3. **Write equations:** $$n + d = 20$$ $$5n + 10d = 165$$ 4. **Solve the system:** From the first equation, express $n$: $$n = 20 - d$$ 5. Substitute into the second equation: $$5(20 - d) + 10d = 165$$ $$100 - 5d + 10d = 165$$ $$100 + 5d = 165$$ 6. Isolate $d$: $$5d = 165 - 100$$ $$5d = 65$$ 7. Divide both sides by 5: $$d = \cancel{\frac{5d}{5}} = \frac{65}{5} = 13$$ 8. **Answer:** Maria has 13 dimes. --- 1. **State the problem:** Tom has five more quarters than dimes, total value 475 cents. Find the number of quarters. 2. **Define variables:** Let $q$ = number of quarters, $d$ = number of dimes. 3. **Write equations:** $$q = d + 5$$ $$25q + 10d = 475$$ 4. Substitute $q$ into the value equation: $$25(d + 5) + 10d = 475$$ $$25d + 125 + 10d = 475$$ $$35d + 125 = 475$$ 5. Isolate $d$: $$35d = 475 - 125$$ $$35d = 350$$ 6. Divide both sides by 35: $$d = \cancel{\frac{35d}{35}} = \frac{350}{35} = 10$$ 7. Find $q$: $$q = d + 5 = 10 + 5 = 15$$ 8. **Answer:** Tom has 15 quarters.