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.