To determine the number of tickets at which the cost of the membership option equals the cost of the regular ticket option, we can set up an equation.
Let \( x \) be the number of tickets.
Cost of regular tickets: \[ \text{Cost} = 7.50x \]
Cost of membership tickets: The initial fee is $30 and the membership ticket price is $5: \[ \text{Cost} = 30 + 5x \]
Now, we can set the two costs equal to each other to find the point at which they are the same:
\[ 7.50x = 30 + 5x \]
Now, let's solve for \( x \):
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Subtract \( 5x \) from both sides: \[ 7.50x - 5x = 30 \] \[ 2.50x = 30 \]
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Now divide by 2.50: \[ x = \frac{30}{2.50} \] \[ x = 12 \]
So, after 12 tickets, both options will cost the same price.