To find the number of tickets after which both options cost the same, we can set up an equation for the total cost of each option.
Let \( n \) be the number of tickets purchased.
For the first option:
- Total cost = Initial fee + Cost per ticket × Number of tickets
- Total cost = \( 20 + 7.50n \)
For the second option:
- Total cost = Initial fee + Cost per ticket × Number of tickets
- Total cost = \( 40 + 5n \)
We want to find the value of \( n \) where both costs are equal: \[ 20 + 7.50n = 40 + 5n \]
Now, we can solve this equation:
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Subtract \( 5n \) from both sides: \[ 20 + 2.50n = 40 \]
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Subtract 20 from both sides: \[ 2.50n = 20 \]
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Divide by 2.50: \[ n = \frac{20}{2.50} = 8 \]
Thus, the two options will cost the same when purchasing 8 tickets.