To find the total amount \( a \) that Mike paid for buying 8 yards of red ribbon at a cost of $3.50 per yard, you can use the equation:
\[ a = \text{(cost per yard)} \times \text{(number of yards)} \]
In this case:
\[ a = 3.50 \times 8 \]
Now, calculate the total amount:
\[ a = 3.50 \times 8 = 28.00 \]
Thus, the amount \( a \) that Mike paid for buying 8 yards of ribbon is:
\[ \boxed{28.00} \]