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)
1. You have plans to attend 3 times this summer. Which option is best?
2. You think you will visit probably about 8 times this summer. Which option is best?
3. You have budgeted $150 for visiting the park this summer. Which option is best?
4. How many visits would be approximately the break even point where both options would cost about the same?
A. Pay per visit
B. Buy a membership
C. 2
D. 15
E. 7
F. 11
To determine which option is best, we need to compare the total cost of each option for the given scenarios.
1. If you plan to attend 3 times this summer:
- Option 1: Pay per visit
Total cost = $28 x 3 = $84
- Option 2: Buy a membership
Total cost = $90 (membership fee) + $15 x 3 (visit cost) = $135
In this case, Option 1 (Pay per visit) is the best option.
2. If you think you will visit about 8 times this summer:
- Option 1: Pay per visit
Total cost = $28 x 8 = $224
- Option 2: Buy a membership
Total cost = $90 (membership fee) + $15 x 8 (visit cost) = $210
In this case, Option 2 (Buy a membership) is the best option.
3. If you have budgeted $150 for visiting the park this summer:
- Option 1: Pay per visit
You can calculate approximately how many visits you can have with $150:
Number of visits = $150 / $28 ≈ 5.36 (rounded down to 5 visits)
Total cost = $28 x 5 = $140
- Option 2: Buy a membership
Total cost = $90 (membership fee) + $15 x 5 (visit cost) = $165
In this case, Option 1 (Pay per visit) is the best option.
4. To find the break-even point where both options cost about the same:
Let the number of visits be N.
Option 1 (Pay per visit) cost = $28N
Option 2 (Buy a membership) cost = $90 + $15N
Set the costs equal to each other and solve for N:
$28N = $90 + $15N
$28N - $15N = $90
$13N = $90
N ≈ 6.92
Since you can't have a fraction of a visit, the break-even point is approximately 7 visits.
Therefore, the answer to question 4 is E (7).
To determine the best option for each scenario, we will compare the total costs of each option.
1. If you plan to attend 3 times this summer, let's compare the costs:
- Pay per visit: 3 visits * $28/visit = $84
- Buy a membership: $90 (membership fee) + 3 visits * $15/visit = $90 + $45 = $135
In this case, the pay per visit option is more cost-effective.
2. If you think you will visit about 8 times this summer, let's compare the costs:
- Pay per visit: 8 visits * $28/visit = $224
- Buy a membership: $90 (membership fee) + 8 visits * $15/visit = $90 + $120 = $210
In this case, the buy a membership option is more cost-effective.
3. If you have budgeted $150 for visiting the park this summer, let's compare the costs:
- Pay per visit: Number of visits * $28/visit = Maximum number of visits within budget * $28/visit = $150/$28 = approximately 5 visits
- Buy a membership: $90 (membership fee) + Number of visits * $15/visit = $90 + Maximum number of visits within budget * $15/visit
In this case, if the maximum number of visits within budget is less than or equal to 5, the pay per visit option is more cost-effective. If the maximum number of visits within budget is more than 5, the buy a membership option is more cost-effective.
4. To find the break-even point where both options would cost about the same, we can set up an equation:
$90 + x * $15 = x * $28
Simplify the equation:
$90 + $15x = $28x
Move all terms involving x to one side:
$28x - $15x = $90
Simplify further:
$13x = $90
Divide both sides of the equation by $13:
x = $90/$13
Approximately, x ≈ 6.92
So, the break-even point is around 7 visits.
To summarize:
- If you plan to attend 3 times, the pay per visit option is best.
- If you plan to attend 8 times, the buy a membership option is best.
- If your budget is $150, and you plan to visit 5 times or less, the pay per visit option is best. If you plan to visit more than 5 times, the buy a membership option is best.
- The break-even point, where both options cost about the same, is approximately 7 visits.
To determine which option is best in each scenario, we need to calculate the cost for each option and compare them.
1. For 3 visits:
- Pay per visit: $28 x 3 = $84
- Membership + pay per visit: $90 + ($15 x 3) = $135
The pay per visit option is cheaper.
2. For 8 visits:
- Pay per visit: $28 x 8 = $224
- Membership + pay per visit: $90 + ($15 x 8) = $210
The membership + pay per visit option is cheaper.
3. With a budget of $150:
- Pay per visit: The number of visits possible is 150 / 28 = 5.36 visits (approximately).
- Membership + pay per visit: The number of visits possible is (150 - 90) / 15 = 4 visits.
The pay per visit option allows for more visits within the budget.
4. To find the break-even point, we need to find the number of visits where the cost of both options is approximately the same. Let's use a formula to calculate this:
28v = 90 + 15v
28v - 15v = 90
13v = 90
v ≈ 6.92
Therefore, the break-even point is approximately 7 visits.
To summarize the answers:
1. Pay per visit
2. Membership + pay per visit
3. Pay per visit
4. 7 visits
So the final answers are:
1. Pay per visit is best.
2. Membership + pay per visit is best.
3. Pay per visit is best.
4. Approximately 7 visits would be the break-even point.