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?
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.
To determine which option is best in each scenario, we can calculate the total cost for each option and compare them.
Scenario 1: You plan to attend 3 times this summer.
Option 1: Paying $28 per visit, the total cost would be 3 * $28 = $84.
Option 2: Purchasing a monthly membership for $90 and paying $15 per visit, the total cost would be $90 + 3 * $15 = $135.
In this case, Option 1 is the best choice because it is cheaper than Option 2.
Scenario 2: You think you will visit approximately 8 times this summer.
Option 1: Paying $28 per visit, the total cost would be 8 * $28 = $224.
Option 2: Purchasing a monthly membership for $90 and paying $15 per visit, the total cost would be $90 + 8 * $15 = $210.
In this case, Option 2 is the best choice because it is cheaper than Option 1.
Scenario 3: You have budgeted $150 for visiting the park this summer.
Option 1: Paying $28 per visit, you can visit the park a maximum of $150 / $28 = 5.36 times. Since you cannot attend a fraction of a time, you can only attend 5 times. The total cost would be 5 * $28 = $140.
Option 2: Purchasing a monthly membership for $90 and paying $15 per visit, you can attend a maximum of ($150 - $90) / $15 = 4 times. The total cost would be $90 + 4 * $15 = $150.
In this case, Option 2 is the best choice because it is within your budget while Option 1 exceeds it.
Scenario 4: Break-even point.
To find the break-even point, we need to set the costs of both options equal to each other.
Let x represent the number of visits.
Option 1: Total cost = $28 * x.
Option 2: Total cost = $90 + $15 * x.
Setting these equations equal to each other:
$28 * x = $90 + $15 * x.
$13 * x = $90.
x = $90 / $13 ≈ 6.92.
Therefore, the break-even point is approximately 7 visits, where both options cost about the same.
To determine which option is the best, we can compare the total cost for each option based on the given scenarios.
Scenario 1: Plans to attend 3 times this summer
Option 1: Paying per visit
Total cost = 3 * $28 = $84
Option 2: Purchasing monthly membership + paying per visit
Total cost = $90 (membership) + 3 * $15 (per visit) = $90 + $45 = $135
Based on this scenario, the option of paying per visit is more cost-effective.
Scenario 2: Plans to visit approximately 8 times this summer
Option 1: Paying per visit
Total cost = 8 * $28 = $224
Option 2: Purchasing monthly membership + paying per visit
Total cost = $90 (membership) + 8 * $15 (per visit) = $90 + $120 = $210
In this scenario, purchasing the monthly membership and paying per visit is more cost-effective.
Scenario 3: Budgeted $150 for visiting the park this summer
Option 1: Paying per visit
The maximum number of visits that can be afforded is $150 / $28 = 5.36 (round down to 5)
Option 2: Purchasing monthly membership + paying per visit
Total cost = $90 (membership) + 5 * $15 (per visit) = $90 + $75 = $165
In this scenario, paying per visit is more cost-effective as it fits within the budget.
To determine the break-even point where both options cost about the same, we need to compare the costs of each option as the number of visits increases.
Let's assume x represents the number of visits.
Option 1: Paying per visit
Total cost = x * $28
Option 2: Purchasing monthly membership + paying per visit
Total cost = $90 (membership) + x * $15
Setting the two total costs equal to each other, we can solve for x:
x * $28 = $90 + x * $15
Simplifying the equation:
$28x = $90 + $15x
Combining like terms:
$28x - $15x = $90
Simplifying further:
$13x = $90
Solving for x:
x = $90 / $13
x ≈ 6.92
Therefore, the break-even point where both options would cost about the same is approximately 7 visits.
i forgot to add the respondes:
:: Pay per visit
:: buy a membership
:: 2
:: 5
:: 7
:: 11
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.