To find the original cost of the groceries \( n \), we need to understand the relationship between the original cost, the coupon discount, and the amount paid after applying the discount.
Nick received a coupon for $15.50 off the original cost \( n \). After applying the coupon, he paid $34.63. This leads us to the equation:
\[ n - 15.50 = 34.63 \]
Now, to find the original cost \( n \), we can rearrange the equation:
\[ n = 34.63 + 15.50 \] \[ n = 50.13 \]
Therefore, the correct equation representing the original cost of groceries Nick bought is:
\( n - 15.50 = 34.63 \); the original cost of the groceries Nick bought was $50.13.