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)
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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?
You have plans to attend 3 times this summer. Which option is best?
Option 1: 3 visits x $28/visit = $<<3*28=84>>84
Option 2: $90 for the membership + 3 visits x $15/visit = $<<90+3*15=135>>135
The best option is Option 1.
You think you will visit probably about 8 times this summer. Which option is best?
Option 1: 8 visits x $28/visit = $<<8*28=224>>224
Option 2: $90 for the membership + 8 visits x $15/visit = $<<90+8*15=210>>210
The best option is Option 2.
You have budgeted $150 for visiting the park this summer. Which option is best?
Option 1: $150 / $28/visit = <<150/28=5.36>>5.36 visits (rounded to the nearest whole number: 5 visits)
Option 2: $90 for the membership + 5 visits x $15/visit = $<<90+5*15=165>>165
The best option is Option 1.
How many visits would be approximately the break-even point where both options would cost about the same?
Let's assume the number of visits required for the break-even point is x.
Option 1: $90 for the membership + x visits x $15/visit = $90 + $15x
Option 2: x visits x $28/visit = $28x
To find the break-even point, we set the two options equal to each other:
$90 + $15x = $28x
Solving for x:
$90 = $28x - $15x
$90 = $13x
x ≈ <<90/13=6.92>>6.92 visits (rounded to the nearest whole number: 7 visits)
Therefore, the break-even point is approximately 7 visits.
To determine which option is best in each scenario, we need to compare the total cost of each option. Let's calculate the total cost for each given situation:
1. You have plans to attend 3 times this summer:
For the single visit option: 3 visits x $28/visit = $84
For the monthly membership option: $90 (membership fee) + 3 visits x $15/visit = $135
Comparing the total costs, the single visit option is better in this scenario.
2. You think you will visit about 8 times this summer:
For the single visit option: 8 visits x $28/visit = $224
For the monthly membership option: $90 (membership fee) + 8 visits x $15/visit = $210
Comparing the total costs, the monthly membership option is better in this scenario.
3. You have budgeted $150 for visiting the park this summer:
For the single visit option: $150 / $28/visit ≈ 5.36 visits
Since you cannot have a fraction of a visit, you would round down to 5 visits for the single visit option.
For the monthly membership option: $90 (membership fee) + 5 visits x $15/visit = $165
Comparing the total costs, the single visit option is better in this scenario.
4. To find the approximate break-even point, we need to set up an equation where the total costs of both options are equal. Let's denote the number of visits as "x" and the total cost as "C."
For the single visit option: C = x visits x $28/visit
For the monthly membership option: C = $90 (membership fee) + x visits x $15/visit
Setting these two equations equal to each other:
x visits x $28/visit = $90 (membership fee) + x visits x $15/visit
Simplifying the equation:
$28x = $90 + $15x
Bringing the "x" terms to one side and the constant terms to the other side:
$28x - $15x = $90
$13x = $90
Dividing both sides by $13 to solve for "x":
x ≈ $90/$13 ≈ 6.92
The approximate break-even point is around 7 visits. After 7 visits, the monthly membership option becomes more cost-effective.
Please note that while this analysis considers only the cost aspect, other factors such as convenience, benefits of membership, and personal preferences should also be taken into account when making a decision.
You have plans to attend 3 times this summer. Which option is best?
Option 1: Paying per visit
Total cost: 3 visits * $28 per visit = $84
Option 2: Monthly membership + paying per visit
Total cost: $90 (monthly membership) + 3 visits * $15 per visit = $135
Option 1 is the best for 3 visits as it is cheaper ($84) compared to Option 2 ($135).
You think you will visit probably about 8 times this summer. Which option is best?
Option 1: Paying per visit
Total cost: 8 visits * $28 per visit = $224
Option 2: Monthly membership + paying per visit
Total cost: $90 (monthly membership) + 8 visits * $15 per visit = $210
Option 2 is the best for 8 visits as it is cheaper ($210) compared to Option 1 ($224).
You have budgeted $150 for visiting the park this summer. Which option is best?
Option 1: Paying per visit
Number of visits within budget: $150 budget / $28 per visit = 5.36 visits (round up to 6 visits)
Total cost: 6 visits * $28 per visit = $168
Option 2: Monthly membership + paying per visit
Number of visits within budget: $150 budget - $90 (monthly membership) = $60 / $15 per visit = 4 visits
Total cost: $90 (monthly membership) + 4 visits * $15 per visit = $150
Option 2 is the best within a $150 budget as it is cheaper ($150) compared to Option 1 ($168).
How many visits would be approximately the break-even point where both options would cost about the same?
Let's assume the break-even point is when the total cost for both options is equal.
Option 1: Paying per visit
Total cost: x visits * $28 per visit = $28x
Option 2: Monthly membership + paying per visit
Total cost: $90 (monthly membership) + x visits * $15 per visit = $90 + $15x
To find the break-even point, we need to solve the equation:
$28x = $90 + $15x
Combining like terms:
$28x - $15x = $90
Simplifying:
$13x = $90
Dividing both sides by $13:
x = $90 / $13
The break-even point is approximately 6.92 visits. Since it's not possible to visit a fraction of a time, the break-even point would be around 7 visits.