To find out after how many tickets both pricing options are the same, we can let \( n \) represent the number of tickets purchased.
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Normal ticket price: The cost per ticket is \( 11 \) dollars, so the cost for \( n \) tickets is: \[ \text{Cost}_\text{normal} = 11n \]
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Membership ticket price: The membership has an initial fee of \( 60 \) dollars and a cost of \( 8.50 \) dollars per ticket. So the total cost for \( n \) tickets with the membership is: \[ \text{Cost}_\text{membership} = 60 + 8.50n \]
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Setting the costs equal: We want to find \( n \) such that: \[ 11n = 60 + 8.50n \]
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Solving for \( n \): First, subtract \( 8.50n \) from both sides: \[ 11n - 8.50n = 60 \] This simplifies to: \[ 2.5n = 60 \]
Next, divide both sides by \( 2.5 \): \[ n = \frac{60}{2.5} = 24 \]
Thus, the two options will cost the same after purchasing 24 tickets.