A movie theater offers a special pricing for membership. The normal cost is $10 per ticket. The membership costs $5 per ticket but an initial fee of $50 . After how many tickets are both options the same price?

Answer 1

Let \( n \) be the number of tickets purchased.

The total cost for buying tickets without a membership is: \[ C_{\text{normal}} = 10n \]

The total cost for buying tickets with a membership is: \[ C_{\text{membership}} = 50 + 5n \]

To find when both options cost the same, we set these two equations equal to each other: \[ 10n = 50 + 5n \]

Now, let's solve for \( n \):

1. Subtract \( 5n \) from both sides: \[ 10n - 5n = 50 \] \[ 5n = 50 \]

2. Divide both sides by 5: \[ n = 10 \]

Therefore, after purchasing 10 tickets, both options will have the same total cost.