Linear Equations, Inequalities and Systems

Some treasure has been buried at a point $${(x,y)}$$ on the grid, where $$x$$ and $$y$$ are whole numbers. 

Here are three clues to help you find the treasure: 
Clue 1:   $$x> 2$$
Clue 2:   $$x+y< 8$$
Clue 3:   $$2y-x\geq 0$$

Which of the following points could be a possible location for the treasure? 

$${(3,2) }$$     $${(2,3)}$$     $${(5,3)}$$      $${(3,5)}$$     $${(4,3)}$$     $${(5,2)}$$

Write a system of linear inequalities that only has the region named as part of the solution set. 

Mary babysits for $4 per hour. She also works as a tutor for $7 per hour. She is only allowed to work 13 hours per week. She wants to make at least $65. Write and graph a system of inequalities to represent this situation.

Fishing Adventures rents small fishing boats to tourists for day-long fishing trips. Each boat can hold at most eight people. Additionally, each boat can only carry 1,200 pounds of people and gear for safety reasons. Assume an average an adult weighs 150 pounds and a child weighs 75 pounds. Also assume each group will require 200 pounds of gear plus 10 pounds of gear per person.

1. Write an inequality that illustrates the weight limit for a group of adults and children on the fishing boat and a second inequality that represents the total number of passengers in the fishing boat. Graph and identify at least one solution to the system of inequalities.
2. Several groups of people wish to rent a boat. Group 1 has 4 adults and 2 children. Group 2 has 3 adults and 5 children. Group 3 has 8 adults. Which of the groups, if any, can safely rent a boat? What other combinations of adults and children are possible?