To determine after how many tickets both membership options cost the same, we can set up an equation.
Let \( x \) represent the number of tickets purchased.
For the first option, the total cost is given by: \[ \text{Cost}_1 = 20 + 15x \]
For the second option, the total cost is: \[ \text{Cost}_2 = 50 + 10x \]
We want to find the value of \( x \) where both costs are equal: \[ 20 + 15x = 50 + 10x \]
Now, we'll solve for \( x \):
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Subtract \( 10x \) from both sides: \[ 20 + 15x - 10x = 50 \] Simplifying gives: \[ 20 + 5x = 50 \]
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Subtract 20 from both sides: \[ 5x = 30 \]
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Divide by 5: \[ x = 6 \]
Thus, after purchasing 6 tickets, both options will cost the same.
Answer: 6 tickets