A movie theater offers two options for membership. The first option costs $15 per ticket but an initial fee of $20. The second option costs $10 per ticket but an initial fee of $50. After how many tickets are both options the same price?

Question

________tickets

Answer 1

To determine after how many tickets both membership options cost the same, we can set up an equation.

Let \( x \) represent the number of tickets purchased.

For the first option, the total cost is given by: \[ \text{Cost}_1 = 20 + 15x \]

For the second option, the total cost is: \[ \text{Cost}_2 = 50 + 10x \]

We want to find the value of \( x \) where both costs are equal: \[ 20 + 15x = 50 + 10x \]

Now, we'll solve for \( x \):

1. Subtract \( 10x \) from both sides: \[ 20 + 15x - 10x = 50 \] Simplifying gives: \[ 20 + 5x = 50 \]

2. Subtract 20 from both sides: \[ 5x = 30 \]

3. Divide by 5: \[ x = 6 \]

Thus, after purchasing 6 tickets, both options will cost the same.

Answer: 6 tickets