First, let's calculate the total amount of yarn Shawna bought:
\[ \text{Total yarn} = \text{Number of balls} \times \text{Yards per ball} = 8 \times 185 \text{ yards} = 1480 \text{ yards} \]
Next, we will determine how much yarn Shawna will have left after she knits the blanket:
\[ \text{Yarn left} = \text{Total yarn} - \text{Yarn needed for the blanket} = 1480 \text{ yards} - 1370 \text{ yards} = 110 \text{ yards} \]
Now, we will check if this leftover yarn is enough to knit the scarf:
\[ \text{Yarn needed for the scarf} = 125 \text{ yards} \]
Since Shawna has 110 yards left, which is less than the 125 yards required for the scarf, we can conclude:
Shawna will have 110 yards of yarn left after she knits the blanket, which is not enough to knit the scarf.