To find the original cost of the groceries, we can use the information provided to set up the appropriate equation.
- Let \( a \) be the original cost of groceries.
- Nick had a coupon for $15.50 off.
- After applying the coupon, Nick paid $34.63.
The equation we can set up is:
\[ a - 15.50 = 34.63 \]
To find the original cost of the groceries \( a \), we can rearrange this equation to solve for \( a \):
\[ a = 34.63 + 15.50 \]
Calculating this gives:
\[ a = 50.13 \]
So the original cost of the groceries Nick bought was $50.13.