To find the number of adult tickets sold, we can substitute the number of student tickets (b) into the equation and solve for the number of adult tickets (a).
We have the equation:
\[ 10.50a + 3.75b = 2071.50 \]
Given that \( b = 82 \), we can substitute this value into the equation:
\[ 10.50a + 3.75(82) = 2071.50 \]
Now, calculate \( 3.75 \times 82 \):
\[ 3.75 \times 82 = 307.50 \]
So the equation becomes:
\[ 10.50a + 307.50 = 2071.50 \]
Next, we subtract 307.50 from both sides:
\[ 10.50a = 2071.50 - 307.50 \]
Calculating the right side:
\[ 2071.50 - 307.50 = 1764 \]
Now our equation is:
\[ 10.50a = 1764 \]
Finally, we divide both sides by 10.50 to find \( a \):
\[ a = \frac{1764}{10.50} \]
Calculating this gives:
\[ a = 168 \]
Thus, the number of adult tickets sold is \( \boxed{168} \).