Question

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?

Answer 1

To determine which option is best in each scenario, we need to compare the total cost of each option.

First scenario (planning to visit 3 times):
Option 1: 3 visits * $28/visit = $<<3*28=84>>84
Option 2: $90 (membership) + 3 visits * $15/visit = $90 + $<<3*15=45>>45 = $135

In this scenario, option 1 is the best choice as it costs $84, which is cheaper than option 2.

Second scenario (planning to visit 8 times):
Option 1: 8 visits * $28/visit = $<<8*28=224>>224
Option 2: $90 (membership) + 8 visits * $15/visit = $90 + $<<8*15=120>>120 = $210

In this scenario, option 2 is the best choice as it costs $210, which is cheaper than option 1.

Third scenario (budgeted $150):
Option 1: $150 / $28/visit ≈ 5.36 visits (round up to 6 visits)
Option 2: $90 (membership) + 6 visits * $15/visit = $90 + $<<6*15=90>>90 = $180

In this scenario, option 1 is the best choice as it costs $150, which is cheaper than option 2.

Lastly, to find the break-even point where both options would cost about the same, we can equate the total costs of both options and solve for the number of visits:
$90 + x * $15 = $28 * x
$90 + $15x = $28x
$90 = $28x - $15x
$90 = $13x
x ≈ 6.92

Therefore, the break-even point is approximately 7 visits, where both options would cost about the same.

Answer 2

i forgot to add the respondes:
:: Pay per visit
:: buy a membership
:: 2
:: 5
:: 7
:: 11

Answer 3

Apologies for the confusion. Here are the responses to each scenario:

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

Option 2: Buy a membership
Total cost = $90 (membership) + 3 * $15 (per visit) = $90 + $45 = $135

Option 1 is the best choice with a total cost of $84.

Scenario 2: Pay 8 visits
Option 1: Pay per visit
Total cost = 8 * $28 = $224

Option 2: Buy a membership
Total cost = $90 (membership) + 8 * $15 (per visit) = $90 + $120 = $210

Option 2 is the best choice with a total cost of $210.

Scenario 3: Budget of $150
Option 1: Pay per visit
The maximum number of visits within the budget is $150 / $28 = 5.36 (round down to 5)

Option 2: Buy a membership
Total cost = $90 (membership) + 5 * $15 (per visit) = $90 + $75 = $165

Option 1 is the best choice as it fits within the budget with a total cost of $140.

Break-even point: Both options cost about the same
Around 7 visits is the break-even point where both options would have a similar total cost.