Seascapes rent small fishing boats for a day-long fishing trips. each boat can carry only 1200 lb of people and gear for safety reasons. assume the average weight of a person is 150 lb. each group will require 200 pounds of gear for the boat plus 10 lb of gear for each person. a) create any quality describing the restrictions on the number of people that can possibly fit in a rented boat. b) several groups of people wish to rent a boat group one has 4 people group two has 5 people group three has 8 people. determine which of the groups, if any, can safely run a boat what is the maximum number of people that may rent a boat.

A. We are given that each person weighs 150 lb, each gear per person weighs 10 lb, and a total of 200 pounds of gear for the boat itself.

Since each person only carries one gear, therefore total weight per person in 160 lb (weight of person + weight of gear).

So let us say that x is the number of persons, the inequality equation is:

160 x + 200 ≤ 1200

B. There are three groups that wish to rent the boat.

> Solve the inequality equation when x = 4

160 (4) + 200 ≤ 1200

840 ≤ 1200           (TRUE)

> Solve the inequality equation when x = 5

160 (5) + 200 ≤ 1200

1000 ≤ 1200         (TRUE)

> Solve the inequality equation when x = 8

160 (8) + 200 ≤ 1200

1480 ≤ 1200         (FALSE)

So only the 4 people group and 5 people group can safely run the boat.

C. Find the maximum number of people that may safely use the boat, solve for x:

160 x + 200 ≤ 1200

160 x ≤ 1000

x ≤ 6.25

Therefore the maximum number of people that can safely use the boat is 6 people.