The first option costs $7.50 per ticket but an initial fee of $20. The second option costs $5 per ticket but an initial fee of $40 . After how many tickets are both options the same price?

Answer 1

To find the number of tickets after which both options cost the same, we can set up an equation for the total cost of each option.

Let \( n \) be the number of tickets purchased.

For the first option:

• Total cost = Initial fee + Cost per ticket × Number of tickets
• Total cost = \( 20 + 7.50n \)

For the second option:

• Total cost = Initial fee + Cost per ticket × Number of tickets
• Total cost = \( 40 + 5n \)

We want to find the value of \( n \) where both costs are equal: \[ 20 + 7.50n = 40 + 5n \]

Now, we can solve this equation:

1. Subtract \( 5n \) from both sides: \[ 20 + 2.50n = 40 \]

2. Subtract 20 from both sides: \[ 2.50n = 20 \]

3. Divide by 2.50: \[ n = \frac{20}{2.50} = 8 \]

Thus, the two options will cost the same when purchasing 8 tickets.