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Ms. Jackson wants to rent a small truck for a week. The cost will be 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.

\[
\begin{tabular}{|l|l|l|}
\hline
\multicolumn{1}{|c|}{Vehicle} & Week & Day \\
\hline
Van & \$470 & \$140 \\
\hline
Small Truck & \$490 & \$150 \\
\hline
Medium Truck & \$510 & \$160 \\
\hline
Large Truck & \$535 & \$170 \\
\hline
Oversized Truck & \$565 & \$180 \\
\hline
\end{tabular}
\]

14. Mr. White is renting a medium 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]510 + 160d[/tex] to find how much he will pay for a 12-day rental.

[tex]\$1310[/tex]

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?

12 days

(Type a whole number.)

Answer :

Let's go through the solution for the questions step by step.

Question 14: Mr. White is renting a medium truck for 12 days. We need to find out the total cost for this rental which includes one full week and a few additional days.

1. Weekly Fee: For the medium truck, the weekly fee is \[tex]$510.
2. Daily Fee: The daily fee for a medium truck is \$[/tex]160.
3. Additional Days: Since a week is 7 days long, the number of additional days is [tex]\( 12 - 7 = 5 \)[/tex] days.

Now, calculate the total cost for 12 days:
- Total Cost = Weekly Fee + (Daily Fee × Additional Days)
- Total Cost = \[tex]$510 + (\$[/tex]160 × 5)
- Total Cost = \[tex]$510 + \$[/tex]800
- Total Cost = \[tex]$1310

So, the cost for Mr. White to rent the medium truck for 12 days is \$[/tex]1310.

Question 15: For any vehicle listed, how many days can you rent before it would be less expensive to rent for the week?

To determine this, we need to compare the cost of renting by the day with the weekly fee. We calculate how many days it takes for the daily cost to match the weekly fee.

For each vehicle, calculate:
1. Van: Weekly Fee = \[tex]$470, Daily Fee = \$[/tex]140
- Break-even days: \[tex]$470 ÷ \$[/tex]140 ≈ 3 days
2. Small Truck: Weekly Fee = \[tex]$490, Daily Fee = \$[/tex]150
- Break-even days: \[tex]$490 ÷ \$[/tex]150 ≈ 3 days
3. Medium Truck: Weekly Fee = \[tex]$510, Daily Fee = \$[/tex]160
- Break-even days: \[tex]$510 ÷ \$[/tex]160 ≈ 3 days
4. Large Truck: Weekly Fee = \[tex]$535, Daily Fee = \$[/tex]170
- Break-even days: \[tex]$535 ÷ \$[/tex]170 ≈ 3 days
5. Oversized Truck: Weekly Fee = \[tex]$565, Daily Fee = \$[/tex]180
- Break-even days: \[tex]$565 ÷ \$[/tex]180 ≈ 3 days

For all vehicles, you can rent for approximately 3 days before it becomes cheaper to rent by the week.

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