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?
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For 3 visits, the best option is to pay per visit.
For 8 visits, the best option is to purchase the monthly membership and pay $15 per visit.
For a budget of $150, the best option is to purchase the monthly membership and pay $15 per visit.
The break-even point would be approximately 6 visits.
To determine which option is best for each scenario, let's calculate the total cost for both options.
1. For attending 3 times this summer:
Option 1: 3 visits x $28/visit = $84
Option 2: $90 (monthly membership) + 3 visits x $15/visit = $135
In this case, Option 1 is the better choice.
2. For visiting approximately 8 times this summer:
Option 1: 8 visits x $28/visit = $224
Option 2: $90 (monthly membership) + 8 visits x $15/visit = $210
In this case, Option 2 is the better choice.
3. With a budget of $150:
Option 1: $28/visit -> $150 ÷ $28/visit = 5.36 visits (round up to 6 visits)
Total cost for 6 visits: 6 visits x $28/visit = $168
Option 2: $90 (monthly membership) + $15/visit -> $150 - $90 (monthly membership) = $60
Total additional visits with $60 budget: $60 ÷ $15/visit = 4 visits
Total cost for 4 additional visits: 4 visits x $15/visit = $60
Total cost for option 2: $90 (monthly membership) + $60 (additional visits) = $150
In this case, both options are equal.
4. To find the break-even point where both options cost about the same:
Let's assume the number of visits required to break even is "x."
Option 1: $28/visit -> Total cost = x visits x $28/visit = $28x
Option 2: $90 (monthly membership) + $15/visit -> Total cost = $90 + x visits x $15/visit = $90 + $15x
Setting both equations equal to each other, we can solve for x:
$28x = $90 + $15x
$28x - $15x = $90
$13x = $90
x ≈ 6.92
Therefore, the break-even point is approximately 6.92 visits.
To determine which option is best in each scenario, we can calculate the total cost for both the individual visit option and the monthly membership option.
For the first scenario where you plan to attend 3 times this summer, let's calculate the total cost for both options:
Option 1: Individual Visit
Cost per visit: $28
Number of visits: 3
Total cost: 28 * 3 = $84
Option 2: Monthly Membership
Cost of membership: $90
Cost per visit: $15
Number of visits: 3
Total cost: 90 + (15 * 3) = $135
In this scenario, the individual visit option is cheaper, with a total cost of $84 compared to the total cost of $135 for the monthly membership option, so the individual visit option is the best choice.
For the second scenario where you think you will visit about 8 times this summer, let's calculate the total cost for both options:
Option 1: Individual Visit
Cost per visit: $28
Number of visits: 8
Total cost: 28 * 8 = $224
Option 2: Monthly Membership
Cost of membership: $90
Cost per visit: $15
Number of visits: 8
Total cost: 90 + (15 * 8) = $210
In this scenario, the monthly membership option is cheaper, with a total cost of $210 compared to the total cost of $224 for the individual visit option, so the monthly membership option is the best choice.
For the third scenario where you have budgeted $150 for visiting the park this summer, let's calculate the total cost for both options:
Option 1: Individual Visit
Cost per visit: $28
Maximum number of visits within budget: 150 / 28 = approximately 5.36 visits (round down to 5 visits)
Total cost: 28 * 5 = $140
Option 2: Monthly Membership
Cost of membership: $90
Cost per visit: $15
Maximum number of visits within budget: (150 - 90) / 15 = 4 visits
Total cost: 90 + (15 * 4) = $150
In this scenario, both options are within the budget, but the monthly membership option results in a total cost of $150, which matches your budget exactly. The individual visit option would be slightly cheaper, but since it exceeds your budget, the monthly membership option is the best choice.
Finally, to find the break-even point where both options would cost about the same, let's set the two total costs equal to each other and solve for the number of visits:
Option 1: Total cost = 28 * x, where x is the number of visits.
Option 2: Total cost = 90 + (15 * x), where x is the number of visits.
Setting the two total costs equal to each other and solving for x:
28 * x = 90 + (15 * x)
28x = 90 + 15x
13x = 90
x = 90 / 13
x ≈ 6.92 visits
So, the break-even point where both options would cost about the same is approximately 6.92 visits.