Question

many elevators have a capacity of 4000 pounds. complete parts (a) through (c) below.
b. graph the inequality. because x and y must be positive, limit the graph to quadrant i only. use the graphing tool to graph the inequality.
c. select an ordered pair that satisfies the inequality. what are the coordinates of the pair? what do the coordinates of the pair represent in the given situation? the point satisfies the inequality. the coordinates represent the fact that when children and adults are in the elevator, the elevator is overloaded.

Explanation:

Step1: Assume weight of a child is \(x\) pounds and an adult is \(y\) pounds. Let's assume for simplicity that a child weighs 80 pounds and an adult weighs 200 pounds. The inequality representing the elevator - capacity is \(80x + 200y\leq4000\), or \(2x + 5y\leq100\) (dividing by 40).

Step2: To find a point that satisfies the inequality and represents an over - loaded situation, we can choose a point above the line \(2x + 5y = 100\) in the first quadrant. Let's take the point \((50,10)\).

• Substitute \(x = 50\) and \(y = 10\) into the left - hand side of the inequality \(2x+5y\): \(2\times50 + 5\times10=100 + 50=150\gt100\).

Answer:

The point \((50,10)\) satisfies the inequality. The coordinates represent the fact that when 50 children and 10 adults are in the elevator, the elevator is overloaded.