1. **State the problem:** We need to find how many adult tickets were sold given that a total of 804 tickets were sold, consisting of adult and student tickets, and there were 54 more student tickets sold than adult tickets. 2. **Define variables:** Let $x$ be the number of adult tickets sold. 3. **Express student tickets in terms of $x$:** Since there are 54 more student tickets than adult tickets, student tickets = $x + 54$. 4. **Write the equation for total tickets:** Total tickets sold = adult tickets + student tickets $$x + (x + 54) = 804$$ 5. **Simplify the equation:** $$2x + 54 = 804$$ 6. **Isolate $x$ by subtracting 54 from both sides:** $$2x + \cancel{54} - \cancel{54} = 804 - 54$$ $$2x = 750$$ 7. **Divide both sides by 2 to solve for $x$:** $$\frac{2x}{\cancel{2}} = \frac{750}{\cancel{2}}$$ $$x = 375$$ 8. **Interpret the result:** There were 375 adult tickets sold. **Final answer:** $$\boxed{375}$$