Question
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
Answers
GPT-4o mini
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**.
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**.