2018 AMC 10A Problem 8

Let $x$ be the number of $5$-cent coins that Joe has. Then the number of $10$-cent coins he has is $x + 3.$ Therefore, Joe has $$23 - x - (x + 3) = 20 - 2x$$ $25$-cent coins. The total value of all these coins is $$5x + 10(x + 3) + 25(20 - 2x)$$$$= 530 - 35x.$$ We know that $$530 - 35x = 320 \Rightarrow x = 6.$$ This means that Joe has $20 - 2 \cdot 6 = 8$ $25$-cent coins. Therefore, he has $8 - 6 = 2$ more $25$-cent coins than $5$-cent coins. Thus, C is the correct answer.