An amusement park that you are excited to try is $28 per visit.

You have the option to purchase a monthly membership for $90 and then pay $15 for each visit.
(4 points)

You have plans to attend 3 times this summer.
Which option is best?

You think you will visit probably about 8 times this summer. Which option is best?

You have budgeted $150 for visiting the park this summer. Which option is best?

How many visits would be approximately the break even point where both options would cost about the same?

Word bank:
Pay per visit
Buy a membership
2
5
7
11

1 answer

To determine which option is best in each scenario, we will calculate the total cost for each option and compare.

1. If you plan to attend 3 times this summer:

Option 1: Pay per visit
Total cost = 3 * $28 = $84

Option 2: Buy a membership
Total cost = $90 (monthly membership) + 3 * $15 (each visit) = $135

In this scenario, it is more cost-effective to choose the pay per visit option.

2. If you think you will visit approximately 8 times this summer:

Option 1: Pay per visit
Total cost = 8 * $28 = $224

Option 2: Buy a membership
Total cost = $90 (monthly membership) + 8 * $15 (each visit) = $210

In this scenario, it is more cost-effective to choose the monthly membership option.

3. If you have budgeted $150 for visiting the park this summer:

Option 1: Pay per visit
With the pay per visit option, you can attend a maximum of $150/$28 = 5 visits.

Option 2: Buy a membership
Total cost = $90 (monthly membership) + 5 * $15 (each visit) = $165

In this scenario, it is more cost-effective to choose the pay per visit option.

4. To determine the break-even point where both options cost about the same:

Let's assume the number of visits to be x.

Option 1: Pay per visit
Total cost = x * $28

Option 2: Buy a membership
Total cost = $90 (monthly membership) + x * $15

We need to find the value of x where these two options cost the same:

x * $28 = $90 + x * $15
13x = $90
x = $90/13
x ≈ 6.92 (approximately 7 visits)

Therefore, the break-even point is approximately 7 visits.