Answered

At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Join our Q&A platform and connect with professionals ready to provide precise answers to your questions in various areas. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

The cost of renting a canoe is [tex]$8 for the first hour plus $[/tex]3 for each additional hour.

Which of the following represents this situation, where [tex]$C$[/tex] is the total cost of renting a canoe for [tex]$h$[/tex] hours?

A. [tex]$C = 8h + 3$[/tex]
B. [tex]$C = 3(h - 1) + 8$[/tex]
C. [tex]$C = 3h + 8$[/tex]
D. [tex]$C = 11h$[/tex]

Sagot :

GinnyAnswer
To determine the correct equation representing the total cost [tex]\( C \)[/tex] of renting a canoe for [tex]\( h \)[/tex] hours, given that it costs \[tex]$8 for the first hour and \$[/tex]3 for each additional hour, let's analyze each option step by step.

First, let's break down the cost structure:
- The first hour costs \[tex]$8. - Each additional hour costs \$[/tex]3.

Now, let's evaluate each option:

### Option A: [tex]\( C = 8h + 3 \)[/tex]
- This implies that each of the [tex]\( h \)[/tex] hours costs \[tex]$8, plus an additional flat fee of \$[/tex]3.
- This would mean for any number of hours [tex]\( h \)[/tex], the cost calculation is [tex]\( C = 8h + 3 \)[/tex].
- For [tex]\( h = 1 \)[/tex]: [tex]\( C = 8 \times 1 + 3 = \$11 \)[/tex].
- The first hour should cost \[tex]$8. Thus, this option does not correctly represent the given cost structure. ### Option B: \( C = 3(h - 1) + 8 \) - This correctly captures the cost structure: - \( C = 3(h-1) \) represents the cost for the additional hours. - Adding 8 accounts for the cost of the first hour. - Let’s test this with \( h = 1 \) and \( h = 3 \): - For \( h = 1 \): \( C = 3(1 - 1) + 8 = 3(0) + 8 = \$[/tex]8 \).
- For [tex]\( h = 3 \)[/tex]: [tex]\( C = 3(3 - 1) + 8 = 3(2) + 8 = 6 + 8 = \$14 \)[/tex].
- This method accurately represents the cost structure.

### Option C: [tex]\( C = 3h + 8 \)[/tex]
- This implies a flat fee of \[tex]$8 plus \$[/tex]3 for each of the [tex]\( h \)[/tex] hours.
- For [tex]\( h = 1 \)[/tex]: [tex]\( C = 3 \times 1 + 8 = 3 + 8 = \$11 \)[/tex].
- The first hour should only cost \[tex]$8, thus this option does not correctly represent the given cost structure. ### Option D: \( C = 11h \) - This represents a rate of \$[/tex]11 for each hour.
- For [tex]\( h = 1 \)[/tex]: [tex]\( C = 11 \times 1 = \$11 \)[/tex].
- For [tex]\( h = 2 \)[/tex]: [tex]\( C = 11 \times 2 = \$22 \)[/tex].
- This does not match the cost structure provided.

From the above analysis, it is clear that option B ([tex]\( C = 3(h - 1) + 8 \)[/tex]) correctly represents the given scenario.
Therefore, the correct answer is:

[tex]\( \boxed{B} \)[/tex]
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.