Question

a movie theater offers two options per membership, but the first option cost $7.50 per ticket but in intial of $15 the second option cost five dollars per ticket get an initial fee of $40. How many tickets to both options stay at the same price.

Answer 1

Let's define:

- \( x \): the number of tickets purchased.

**Option 1:**
- Cost: $7.50 per ticket + $15 initial fee
- Total cost for Option 1 = \( 7.50x + 15 \)

**Option 2:**
- Cost: $5.00 per ticket + $40 initial fee
- Total cost for Option 2 = \( 5.00x + 40 \)

We want to find the value of \( x \) where both options cost the same:

\[
7.50x + 15 = 5.00x + 40
\]

Now, we will solve for \( x \):

1. Subtract \( 5.00x \) from both sides:
\[
7.50x - 5.00x + 15 = 40
\]
\[
2.50x + 15 = 40
\]

2. Subtract 15 from both sides:
\[
2.50x = 25
\]

3. Divide both sides by 2.50:
\[
x = \frac{25}{2.50} = 10
\]

Thus, the two options will cost the same when you purchase **10 tickets**.