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?
Word bank:
Pay per visit
Buy a membership
2
5
7
11
To determine which option is best in each scenario, we will calculate the total cost for each option and compare.
1. If you plan to attend 3 times this summer:
Option 1: Pay per visit
Total cost = 3 * $28 = $84
Option 2: Buy a membership
Total cost = $90 (monthly membership) + 3 * $15 (each visit) = $135
In this scenario, it is more cost-effective to choose the pay per visit option.
2. If you think you will visit approximately 8 times this summer:
Option 1: Pay per visit
Total cost = 8 * $28 = $224
Option 2: Buy a membership
Total cost = $90 (monthly membership) + 8 * $15 (each visit) = $210
In this scenario, it is more cost-effective to choose the monthly membership option.
3. If you have budgeted $150 for visiting the park this summer:
Option 1: Pay per visit
With the pay per visit option, you can attend a maximum of $150/$28 = 5 visits.
Option 2: Buy a membership
Total cost = $90 (monthly membership) + 5 * $15 (each visit) = $165
In this scenario, it is more cost-effective to choose the pay per visit option.
4. To determine the break-even point where both options cost about the same:
Let's assume the number of visits to be x.
Option 1: Pay per visit
Total cost = x * $28
Option 2: Buy a membership
Total cost = $90 (monthly membership) + x * $15
We need to find the value of x where these two options cost the same:
x * $28 = $90 + x * $15
13x = $90
x = $90/13
x ≈ 6.92 (approximately 7 visits)
Therefore, the break-even point is approximately 7 visits.
To determine which option is the best in each scenario, let's compare the total cost of each option.
1. Attending 3 times this summer:
a) Pay per visit: Cost = $28 x 3 = $84
b) Buy a monthly membership: Cost = Membership ($90) + Visits ($15 x 3) = $90 + $45 = $135
In this case, the pay per visit option is best as it costs $84 compared to $135 with the membership option.
2. Attending 8 times this summer:
a) Pay per visit: Cost = $28 x 8 = $224
b) Buy a monthly membership: Cost = Membership ($90) + Visits ($15 x 8) = $90 + $120 = $210
In this case, the membership option is best as it costs $210 compared to $224 with the pay per visit option.
3. Budgeted $150 for visiting the park this summer:
a) Pay per visit: You can visit the park a maximum of $150 / $28 = about 5 times.
The cost for 5 visits would be $28 x 5 = $140.
b) Buy a monthly membership: With the membership, you would not be able to stay within your budget as the cost would be Membership ($90) + Visits ($15 x 5) = $90 + $75 = $165.
In this case, the pay per visit option is best as it allows you to stay within your budget.
4. Break-even point where both options cost about the same:
Let's say the number of visits needed to break even is X.
a) Pay per visit: Cost = $28 x X
b) Buy a monthly membership: Cost = Membership ($90) + Visits ($15 x X)
To find the break-even point, we can set the pay per visit option equal to the membership option and solve for X:
$28x = $90 + $15x
$13x = $90
X ≈ 6.9
Therefore, the break-even point is approximately 7 visits, where both options would cost about the same.
To determine which option is best, we need to compare the total cost of each option for different scenarios. Let's calculate the cost for each scenario:
1. Visiting the park 3 times:
- Pay per visit: 3 visits x $28 per visit = $84
- Buy a membership: $90 (membership fee) + 3 visits x $15 per visit = $135
In this case, the "Pay per visit" option is more cost-effective, as it costs $84 compared to $135 with the membership.
2. Visiting the park around 8 times:
- Pay per visit: 8 visits x $28 per visit = $224
- Buy a membership: $90 (membership fee) + 8 visits x $15 per visit = $210
In this scenario, the "Buy a membership" option is more cost-effective since it costs $210 compared to $224 with the pay per visit option.
3. Having a budget of $150:
- Pay per visit: The maximum number of visits you can afford is $150 ÷ $28 per visit ≈ 5.36 visits. Since you cannot visit a fraction of a time, the maximum number of visits would be 5.
- Buy a membership: With a budget of $150, you can only afford the membership fee of $90, which means you won't be able to visit the park any additional times.
In this case, neither option allows you to fully utilize your budget. However, if you still want to maximize the number of visits within your budget, the "Pay per visit" option would be better as you can have 5 visits for $140.
4. Break even point:
To find the break-even point, we need to determine the number of visits where the total cost for both options would be approximately equal. Let's set up an equation to solve for this:
$90 + $15x = $28x
Where x represents the number of visits.
Simplifying the equation, we get:
$90 = $28x - $15x
$90 = $13x
x = $90 ÷ $13 ≈ 6.92 visits
Approximately 7 visits would be the break-even point where both options cost about the same.
In conclusion:
- If you plan to visit 3 times, the "Pay per visit" option is better.
- If you plan to visit around 8 times, the "Buy a membership" option is better.
- If you have a budget of $150, the "Pay per visit" option allows for more visits within the budget.
- The break-even point is approximately 7 visits.