Let's denote the number of dimes as \( d \).
According to the problem, there are 32 quarters and it states that there are eight times as many quarters as dimes. This can be expressed as:
\[ 32 = 8d \]
To find the number of dimes \( d \), we can solve this equation:
\[ d = \frac{32}{8} = 4 \]
Thus, there are \( 4 \) dimes in the bag.