1. **State the problem:** We have 70 coins in total, consisting of nickels and dimes, and their total value is 4.65. 2. **Define variables:** Let $n$ be the number of nickels and $d$ be the number of dimes. 3. **Write the system of equations:** - Total coins: $$n + d = 70$$ - Total value in dollars: $$0.05n + 0.10d = 4.65$$ 4. **Solve the system:** From the first equation, express $n$ as $$n = 70 - d$$ Substitute into the second equation: $$0.05(70 - d) + 0.10d = 4.65$$ 5. **Simplify and solve for $d$:** $$3.5 - 0.05d + 0.10d = 4.65$$ $$3.5 + 0.05d = 4.65$$ $$0.05d = 4.65 - 3.5 = 1.15$$ $$d = \frac{1.15}{0.05} = 23$$ 6. **Find $n$:** $$n = 70 - 23 = 47$$ 7. **Answer:** There are 47 nickels and 23 dimes.