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Answer :
To determine how many days you can rent each type of vehicle before it becomes less expensive to rent for the week, let's follow these steps:
1. Understand the Pricing Structure:
- Each vehicle has a different daily and weekly rental rate.
- For each vehicle, we'll compare the cost of renting daily to the weekly rental fee.
2. Determine the Cumulative Daily Cost:
- We'll calculate how much it costs to rent a vehicle for several days using the daily rate.
3. Compare with Weekly Cost:
- For each vehicle, we'll compare the cumulative daily cost to the weekly rental cost.
- We want to find out after how many days of renting daily, the cost would equal or exceed the weekly rental cost.
4. Calculate the Days:
- Let's calculate this for each type of vehicle:
- Van:
- Weekly Cost: [tex]$410
- Daily Cost: $[/tex]120
- After 3 days, the daily cost is [tex]\(3 \times 120 = 360\)[/tex], which is less than [tex]$410.
- After 4 days, the daily cost is \(4 \times 120 = 480\), which is more than $[/tex]410.
- Therefore, it's better to rent weekly if renting for 4 or more days.
- Small Truck:
- Weekly Cost: [tex]$430
- Daily Cost: $[/tex]130
- After 3 days, the daily cost is [tex]\(3 \times 130 = 390\)[/tex], which is less than [tex]$430.
- After 4 days, the daily cost is \(4 \times 130 = 520\), which is more than $[/tex]430.
- Therefore, it's better to rent weekly if renting for 4 or more days.
- Medium Truck:
- Weekly Cost: [tex]$450
- Daily Cost: $[/tex]140
- After 3 days, the daily cost is [tex]\(3 \times 140 = 420\)[/tex], which is less than [tex]$450.
- After 4 days, the daily cost is \(4 \times 140 = 560\), which is more than $[/tex]450.
- Therefore, it's better to rent weekly if renting for 4 or more days.
- Large Truck:
- Weekly Cost: [tex]$475
- Daily Cost: $[/tex]150
- After 3 days, the daily cost is [tex]\(3 \times 150 = 450\)[/tex], which is less than [tex]$475.
- After 4 days, the daily cost is \(4 \times 150 = 600\), which is more than $[/tex]475.
- Therefore, it's better to rent weekly if renting for 4 or more days.
- Oversized Truck:
- Weekly Cost: [tex]$505
- Daily Cost: $[/tex]160
- After 3 days, the daily cost is [tex]\(3 \times 160 = 480\)[/tex], which is less than [tex]$505.
- After 4 days, the daily cost is \(4 \times 160 = 640\), which is more than $[/tex]505.
- Therefore, it's better to rent weekly if renting for 4 or more days.
So, for all vehicles listed, you can rent up to 3 days before it would be less expensive to rent for the week.
1. Understand the Pricing Structure:
- Each vehicle has a different daily and weekly rental rate.
- For each vehicle, we'll compare the cost of renting daily to the weekly rental fee.
2. Determine the Cumulative Daily Cost:
- We'll calculate how much it costs to rent a vehicle for several days using the daily rate.
3. Compare with Weekly Cost:
- For each vehicle, we'll compare the cumulative daily cost to the weekly rental cost.
- We want to find out after how many days of renting daily, the cost would equal or exceed the weekly rental cost.
4. Calculate the Days:
- Let's calculate this for each type of vehicle:
- Van:
- Weekly Cost: [tex]$410
- Daily Cost: $[/tex]120
- After 3 days, the daily cost is [tex]\(3 \times 120 = 360\)[/tex], which is less than [tex]$410.
- After 4 days, the daily cost is \(4 \times 120 = 480\), which is more than $[/tex]410.
- Therefore, it's better to rent weekly if renting for 4 or more days.
- Small Truck:
- Weekly Cost: [tex]$430
- Daily Cost: $[/tex]130
- After 3 days, the daily cost is [tex]\(3 \times 130 = 390\)[/tex], which is less than [tex]$430.
- After 4 days, the daily cost is \(4 \times 130 = 520\), which is more than $[/tex]430.
- Therefore, it's better to rent weekly if renting for 4 or more days.
- Medium Truck:
- Weekly Cost: [tex]$450
- Daily Cost: $[/tex]140
- After 3 days, the daily cost is [tex]\(3 \times 140 = 420\)[/tex], which is less than [tex]$450.
- After 4 days, the daily cost is \(4 \times 140 = 560\), which is more than $[/tex]450.
- Therefore, it's better to rent weekly if renting for 4 or more days.
- Large Truck:
- Weekly Cost: [tex]$475
- Daily Cost: $[/tex]150
- After 3 days, the daily cost is [tex]\(3 \times 150 = 450\)[/tex], which is less than [tex]$475.
- After 4 days, the daily cost is \(4 \times 150 = 600\), which is more than $[/tex]475.
- Therefore, it's better to rent weekly if renting for 4 or more days.
- Oversized Truck:
- Weekly Cost: [tex]$505
- Daily Cost: $[/tex]160
- After 3 days, the daily cost is [tex]\(3 \times 160 = 480\)[/tex], which is less than [tex]$505.
- After 4 days, the daily cost is \(4 \times 160 = 640\), which is more than $[/tex]505.
- Therefore, it's better to rent weekly if renting for 4 or more days.
So, for all vehicles listed, you can rent up to 3 days before it would be less expensive to rent for the week.
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