Question
A movie theater offers two options for membership. The first option costs $15\$15$15 per ticket but an initial fee of $15\$15$15. The second option costs $10\$10$10 per ticket but an initial fee of $45\$45$45 . After how many tickets are both options the same price? Click Here for Help Video
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Answers
GPT-4o mini
Let \( x \) be the number of tickets purchased.
For the first membership option, the total cost can be expressed as:
\[
\text{Cost}_1 = 15 + 15x
\]
This includes an initial fee of $15 and $15 per ticket.
For the second membership option, the total cost can be expressed as:
\[
\text{Cost}_2 = 45 + 10x
\]
This includes an initial fee of $45 and $10 per ticket.
We want to find the number of tickets where the cost of both options is the same:
\[
15 + 15x = 45 + 10x
\]
Now, let's solve the equation:
1. Subtract \( 10x \) from both sides:
\[
15 + 15x - 10x = 45
\]
\[
15 + 5x = 45
\]
2. Subtract 15 from both sides:
\[
5x = 30
\]
3. Divide by 5:
\[
x = 6
\]
Thus, the number of tickets after which both options are the same price is \( \boxed{6} \).
For the first membership option, the total cost can be expressed as:
\[
\text{Cost}_1 = 15 + 15x
\]
This includes an initial fee of $15 and $15 per ticket.
For the second membership option, the total cost can be expressed as:
\[
\text{Cost}_2 = 45 + 10x
\]
This includes an initial fee of $45 and $10 per ticket.
We want to find the number of tickets where the cost of both options is the same:
\[
15 + 15x = 45 + 10x
\]
Now, let's solve the equation:
1. Subtract \( 10x \) from both sides:
\[
15 + 15x - 10x = 45
\]
\[
15 + 5x = 45
\]
2. Subtract 15 from both sides:
\[
5x = 30
\]
3. Divide by 5:
\[
x = 6
\]
Thus, the number of tickets after which both options are the same price is \( \boxed{6} \).