The friends read the sign advertising the boats and learn that each boat has a [choose a weight between 750 pounds and 900 pounds] weight limit. The friends know that they each weigh on average 150 pounds. Write and solve an inequality that represents the number of friends that could fit in each boat. Based on this information, what is the minimum number of boats they need to rent?

2 answers

Let's denote the weight limit of the boat as \( W \). According to your instructions, choose a weight limit; we'll use \( W = 800 \) pounds as an example.

Each friend weighs on average 150 pounds. If \( n \) represents the number of friends, the total weight of \( n \) friends would be \( 150n \) pounds.

To find the inequality representing the number of friends that can fit in one boat, we need:

\[ 150n \leq W \]

Substituting the weight limit we chose:

\[ 150n \leq 800 \]

To solve for \( n \), divide both sides by 150:

\[ n \leq \frac{800}{150} \]

Calculating the right side:

\[ n \leq \frac{800}{150} \approx 5.33 \]

Since \( n \) must be a whole number (you can’t have a fraction of a person), the maximum number of friends that can fit in one boat is 5.

Now, let's assume you have a total of \( T \) friends. To determine the minimum number of boats required, divide the total number of friends by the maximum number of friends per boat. The inequality can be expressed as:

\[ \text{Number of boats} \geq \frac{T}{5} \]

As an example, if there are 20 friends, the minimum number of boats needed would be:

\[ \text{Number of boats} \geq \frac{20}{5} = 4 \]

So, 4 boats would be needed to accommodate 20 friends. Feel free to provide a specific number of friends \( T \) for a more precise calculation!

Use the information from the solutions to your inequalities to write a proposal to the friends about how many boats they should rent. Be sure to explain all their options for the number of boats they could rent, which option you think is best, and why.