To find the unit price of one ballpoint pen, you divide the total cost of the box by the number of pens.
The cost of a box of 10 ballpoint pens is $8.
So,
\[ \text{Unit Price} = \frac{\text{Total Cost}}{\text{Number of Pens}} = \frac{8}{10} = 0.80 \]
Therefore, the cost per pen is $0.80.
The correct answer is A) $0.80/pen.