High School

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Ms. Jackson wants to rent a small truck for a week. It will cost the weekly fee plus [tex]$0.40[/tex] per mile driven. Let [tex]m[/tex] be the number of miles Ms. Jackson drives during the week. Use this information and the table to answer questions 13-15.

\[
\begin{tabular}{|l|c|c|}
\hline
\multicolumn{1}{|c|}{Vehicle} & Week & Day \\
\hline
Van & \$410 & \$120 \\
\hline
Small Truck & \$430 & \$130 \\
\hline
Medium Truck & \$450 & \$140 \\
\hline
Large Truck & \$475 & \$150 \\
\hline
Oversized Truck & \$505 & \$160 \\
\hline
\end{tabular}
\]

14. Mr. White is renting an oversized truck for one week and a few additional days [tex]d[/tex]. He does not have to pay a per mile fee. Evaluate the expression [tex]505 + 160d[/tex] to find how much he will pay for a 12-day rental.

15. For any of the vehicles listed in the table, how many days can you rent before it would be less expensive to rent for the week?

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.

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