Question

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**.