You and your family will be taking a long vacation (from 1 to 4 weeks) to Camotes Island. The place is so small that the residents don't use cars but large enough that they do use other forms of transportation. There are three motorbike rental companies on the island. All three companies have weekly rentals.
Motostarr charges ₱500 upfront (advance payment) plus ₱150 per week
NL & Co charges ₱200 upfront (advance payment) plus ₱250 per week
Sikad charges ₱350 upfront plus ₱200 per week
You must come up with a detailed reason for choosing which company to rent scooters from the island.
Here are your tasks!
Show your family a table with the costs broken down.
Show your family a graph of the costs.
Show your family algebraically how to find the best deal.
After coming up with your choice and convincing your family to go with that company, you receive a coupon in the mail from Sikad with a special offer. The offer is for the use of a jet ski for a day at no charge. The usual daily rental for the jet ski is ₱150. Does this change your decision?
Explain in full detail why this does or does not change your initial decision, what was difficult for you in this task, what you learned, and what you might do differently.
for w weeks, the costs are
Moto: 500+150x
NL: 200+250x
Sikad: 350+200x
Now you can compare the cost when 1 <= x <= 4
1. Table with costs broken down:
| Rental Company | Upfront Cost (₱) | Cost per week (₱) |
|----------------|------------------|------------------|
| Motostarr | 500 | 150 |
| NL & Co | 200 | 250 |
| Sikad | 350 | 200 |
2. Graph of the costs:
(Note: The y-axis represents the total cost in ₱, and the x-axis represents the number of weeks.)
```
|
1000 + -+- NL & Co
| | Sikad
750 + -+---+ Motostarr
| |
--------- Week
```
3. Algebraically finding the best deal:
Let's say the number of weeks of rental is represented by 'w'.
For Motostarr:
Cost = Upfront Cost + (Cost per week x Number of weeks)
C(Motostarr) = 500 + (150w)
For NL & Co:
Cost = Upfront Cost + (Cost per week x Number of weeks)
C(NL & Co) = 200 + (250w)
For Sikad:
Cost = Upfront Cost + (Cost per week x Number of weeks)
C(Sikad) = 350 + (200w)
To find the best deal, we can compare these expressions for different values of 'w' and choose the one with the lowest cost.
4. The Sikad jet ski coupon:
The coupon offers the use of a jet ski for a day at no charge, which usually costs ₱150 per day. This offer does not change the initial decision because it is valid for only one day and does not affect the overall cost of renting the motorbike for the entire vacation.
Full explanation:
Based on the table and the graph, we can visualize the cost differences between the three rental companies. Initially, Motostarr seems to be the most cost-effective option, followed by NL & Co and Sikad. However, to confirm this, we can use algebra to find the best deal.
After comparing the expressions for the cost of each company, we can see that the cost of Sikad (350 + 200w) is always higher than the cost of Motostarr (500 + 150w) for any number of weeks. Hence, the initial decision was to go with Motostarr.
The Sikad jet ski coupon does not change the initial decision because it only offers a one-day rental of the jet ski at no charge. This does not impact the overall cost of renting the motorbike for the vacation.
In this task, there were no significant difficulties. However, it was essential to carefully analyze the costs and understand the terms and conditions of the Sikad coupon. The task reinforced the importance of making informed decisions by considering all factors, such as cost, duration, and any additional offers or deals.
If I were to do something differently, I might consider exploring other factors such as the condition of the motorbikes, customer reviews, and proximity to our accommodation. These factors could influence the rental company choice in addition to cost.
To compare the costs of renting motorbikes from the three companies, let's create a table:
Company | Upfront Cost (₱) | Weekly Cost (₱)
------------|------------------|----------------
Motostarr | 500 | 150
NL & Co | 200 | 250
Sikad | 350 | 200
We can calculate the total cost for each company based on the duration of the vacation (1 to 4 weeks). Let's assume the vacation is for 2 weeks (14 days):
Company | Total Cost (₱)
------------|------------------
Motostarr | 500 + 2 * 150 = 800
NL & Co | 200 + 2 * 250 = 700
Sikad | 350 + 2 * 200 = 750
Now let's plot the costs on a graph:
1 week:
|
| Sikad
|
| NL & Co
|
| Motostarr
. . . . . .
2 weeks:
|
|
|
. . | ---------------- Sikad
. . |
|
. . | ---------- NL & Co
|
|--------- Motostarr
. . . . . . . . . .
3 weeks:
|
. . |---------------- Sikad
. . |
|
. . | ---------- NL & Co
|
|---------- Motostarr
. . . . . . . . . .
4 weeks:
|
. . |---------------- Sikad
. . |
|
. . | ------------ NL & Co
|
|------------ Motostarr
. . . . . . . . . .
From the table and graph, we can see that NL & Co has the lowest cost for a 2-week vacation, followed closely by Sikad and Motostarr.
To find the best deal algebraically, we can use the formula:
Total Cost = Upfront Cost + (Weekly Cost * Number of Weeks)
For example, for NL & Co:
Total Cost = 200 + (250 * 2)
= 700
We can calculate the total costs for each company for different durations and compare to determine the best deal.
Regarding the coupon from Sikad for a free jet ski rental, let's analyze if it changes the initial decision. The coupon states that the jet ski rental costs ₱150 per day. If we assume that we would rent the jet ski for one day, and the vacation duration is still 2 weeks:
- Sikad: Total Cost = 750 (from earlier calculation)
- NL & Co: Total Cost = 200 + (250 * 2) = 700
Even with the free jet ski rental, NL & Co still offers a lower overall cost for the motorbike rentals. Therefore, it does not change the initial decision to go with NL & Co.
In this task, the most challenging part might be comparing the costs and making a decision based on them. It requires careful analysis and consideration of all factors. It is essential to consider not only the upfront cost but also the weekly cost and any additional offers or discounts.
From this task, we learned how to compare costs using a table, graph, and algebraic equations. We also understood the importance of considering additional offers and discounts when making decisions.
If we were to do things differently, we could have considered different vacation durations and compared the costs for each company in more detail. This would provide a more comprehensive analysis and ensure the most cost-effective choice for our motorbike rental.