Question

complete part (e) of the problem proof. let w represent the total weight of a group of people wishing to rent a boat. a) write an inequality that describes all total weights allowed in a boat. b) draw a number line diagram that shows all possible solutions. c) does the inequality you wrote realistically describe the weights of the people?

Explanation:

Step1: Assume boat weight - limit

Let the maximum weight capacity of the boat be \(C\). The inequality for the total weight \(w\) of people allowed in the boat is \(w\leq C\).

Step2: Draw number - line

On a number - line, mark the point \(C\). Draw a solid circle at \(C\) (since \(w = C\) is allowed, due to \(\leq\)) and draw a line to the left of \(C\) to represent all values of \(w\) that satisfy \(w\leq C\).

Step3: Analyze realism

The inequality \(w\leq C\) realistically describes the weights of people in the sense that the total weight of the group of people in the boat cannot exceed the boat's weight - capacity. However, it does not account for other factors like distribution of weight in the boat, etc. But just in terms of total weight, it is a valid and realistic first - order description.

Answer:

a) \(w\leq C\) (where \(C\) is the maximum weight capacity of the boat)
b) Mark point \(C\) on the number - line, draw a solid circle at \(C\) and a line to the left of \(C\).
c) Yes, it is a valid first - order description for total weight, but does not account for all factors.