Final answer:
Nolan would need to visit either performing art center 5 times for the costs to be the same, derived from solving the equation $100 + $15x = $75 + $20x.
Step-by-step explanation:
To find out how many times Nolan would need to visit both performing arts centers for the cost to be the same, we set up an equation where both total costs are equal.
Let x be the number of visits. For the first center, the cost would be $100 + $15x, and for the second center, it would be $75 + $20x.
Set the two costs equal to each other to find the breakeven point:
$100 + $15x = $75 + $20x
Subtract $75 and $15x from both sides to isolate the variable term:
$25 = $5x
Divide by $5 to solve for x:
x = 5
Thus, Nolan would need to visit either of the centers 5 times for the total cost of season pass plus parking to be the same.