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a movie theater offers a special price for membership. The normal cost is $11 per ticket. The membership cost $8.50 per ticket but initial fee of $60. How many tickets are both option the same price

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To find the number of tickets at which both options cost the same, we can set up an equation.

Let \( x \) be the number of tickets.

The total cost for the regular ticket option (without membership) is: \[ \text{Cost}_{\text{regular}} = 11x \]

The total cost for the membership option is: \[ \text{Cost}_{\text{membership}} = 60 + 8.50x \]

To find when these two costs are equal, we set the equations equal to each other: \[ 11x = 60 + 8.50x \]

Now, we can solve for \( x \).

  1. Subtract \( 8.50x \) from both sides: \[ 11x - 8.50x = 60 \] \[ 2.50x = 60 \]

  2. Divide both sides by 2.50: \[ x = \frac{60}{2.50} = 24 \]

So, both options cost the same when you buy 24 tickets.