An amusement park that you are excited to try is %2428 per visit. You have the option to purchase a monthly membership for %2490 and then pay %2415 for each visit. (4 points) Put responses in the correct input to answer the question. Select a response%2C navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar%2C enter key%2C left mouse button or touchpad. Responses can also be moved by dragging with a mouse. You have plans to attend 3 times this summer. Which option is best%3F You think you will visit probably about 8 times this summer. Which option is best%3F You have budgeted %24150 for visiting the park this summer. Which option is best%3F How many visits would be approximately the break even point where both options would cost about the same%3F
To determine which option is best for each scenario, we can calculate the total cost for each option.
Option 1: Pay per visit
Cost per visit: $28
Number of visits planned: 3
Total cost with 3 visits: $28 x 3 = $<<28*3=84>>84
Option 2: Monthly membership + cost per visit
Monthly membership cost: $90
Cost per visit: $15
Number of visits planned: 3
Total cost with 3 visits: $90 + ($15 x 3) = $90 + $45 = $<<90+15*3=135>>135
Therefore, for 3 visits, the pay per visit option is better as it costs $84 compared to $135 with the monthly membership option.
Now let's consider the scenario where you think you will visit the park approximately 8 times this summer.
Option 1: Pay per visit
Cost per visit: $28
Number of visits planned: 8
Total cost with 8 visits: $28 x 8 = $224
Option 2: Monthly membership + cost per visit
Monthly membership cost: $90
Cost per visit: $15
Number of visits planned: 8
Total cost with 8 visits: $90 + ($15 x 8) = $90 + $120 = $<<90+15*8=210>>210
Therefore, for 8 visits, the monthly membership option is better as it costs $210 compared to $224 with the pay per visit option.
Lastly, let's consider the scenario where you have budgeted $150 for visiting the park this summer.
Option 1: Pay per visit
Cost per visit: $28
Number of visits: x
Total cost with x visits: $28x
Option 2: Monthly membership + cost per visit
Monthly membership cost: $90
Cost per visit: $15
Number of visits: x
Total cost with x visits: $90 + ($15x)
We need to find the number of visits, x, where the total cost for both options is approximately the same, so we can set up the equation:
$28x = $90 + ($15x)
Simplifying the equation, we get:
$13x = $90
x = $90 / $13
x ≈ 6.92
Therefore, at approximately 7 visits, both options would cost about the same.
In summary:
- For 3 visits, the pay per visit option is best.
- For 8 visits, the monthly membership option is best.
- At approximately 7 visits, both options would cost about the same.
To determine which option is best, we need to compare the total cost of each option based on the given scenarios. Let's calculate the costs for each scenario:
1. You have plans to attend 3 times this summer:
Option 1: 3 visits x $28 per visit = $84
Option 2: Membership ($90) + 3 visits x $15 per visit = $135
In this case, the first option (paying per visit) is more cost-effective since it costs $84 compared to $135 for the membership option.
2. You think you will visit approximately 8 times this summer:
Option 1: 8 visits x $28 per visit = $224
Option 2: Membership ($90) + 8 visits x $15 per visit = $210
In this case, the second option (purchasing a membership) is more cost-effective as it costs $210 compared to $224 for the pay-per-visit option.
3. You have budgeted $150 for visiting the park this summer:
Option 1: $150 / $28 per visit = 5.36 visits (rounding down to 5)
Option 2: Membership ($90) + 5 visits x $15 per visit = $165
In this case, the first option (paying per visit) is more cost-effective as it costs $150 compared to $165 for the membership option.
4. To find the break-even point:
Let's assume x is the number of visits where both options cost approximately the same.
Option 1: x visits x $28 per visit
Option 2: Membership ($90) + x visits x $15 per visit
Setting the costs equal, we have: x * 28 = 90 + x * 15
Solving for x: 13x = 90
x ≈ 6.92
So, approximately 7 visits would be the break-even point where both options would cost about the same.
In summary:
- For 3 visits, the pay-per-visit option is best.
- For 8 visits, the membership option is best.
- With a budget of $150, the pay-per-visit option is best.
- At approximately 7 visits, both options would cost about the same.
To determine the best option, we can compare the total cost for each scenario:
1. Attending 3 times this summer:
Option 1: Pay per visit
Cost = 3 visits × $28 per visit = $84
Option 2: Monthly membership + per visit fee
Cost = $90 (monthly membership) + 3 visits × $15 per visit = $135
In this case, the pay per visit option is cheaper.
2. Visiting approximately 8 times this summer:
Option 1: Pay per visit
Cost = 8 visits × $28 per visit = $224
Option 2: Monthly membership + per visit fee
Cost = $90 (monthly membership) + 8 visits × $15 per visit = $210
In this case, the monthly membership plus per visit fee option is cheaper.
3. Budgeted $150 for visiting the park this summer:
Option 1: Pay per visit
Cost = Number of visits × $28 per visit
To find the number of visits, we can set up the equation:
$150 = Number of visits × $28
Number of visits = $150 / $28 ≈ 5.36 visits
Since we cannot have a fractional number of visits, we round up to 6 visits.
Option 2: Monthly membership + per visit fee
Cost = $90 (monthly membership) + 6 visits × $15 per visit = $180
In this case, the pay per visit option is cheaper.
4. Break-even point where both options would cost about the same:
Let's assume the number of visits for the break-even point is V.
Option 1 cost = V visits × $28 per visit
Option 2 cost = $90 (monthly membership) + V visits × $15 per visit
To find the break-even point, we can set up the equation:
V visits × $28 per visit = $90 (monthly membership) + V visits × $15 per visit
Solving for V, we get:
$28V = $90 + $15V
$13V = $90
V ≈ $90 / $13 ≈ 6.92 visits
Therefore, the approximate break-even point where both options would cost about the same is around 7 visits.