2004 AMC 10B Problem 15

Swapping increases the value, so Patty has more nickels than dimes. Each swapped coin changes the total by $5$ cents, so she has $\frac{70}{5} = 14$ more nickels than dimes. With $n + d = 20$ and $n - d = 14,$ she has $17$ nickels and $3$ dimes. Her coins are worth $17 \cdot 5 + 3 \cdot 10 = 115$ cents, or $\$1.15.$ Thus, the correct answer is A.