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: Recall Elevator Capacity

Assume children's weight is \( c \) and adults' weight is \( a \). Let \( x \) = number of children, \( y \) = number of adults. If average child weight is 50 lbs, adult is 150 lbs, inequality: \( 50x + 150y \leq 4000 \) → \( x + 3y \leq 80 \) → \( y \leq -\frac{1}{3}x + \frac{80}{3} \).

Step2: Choose Ordered Pair

Pick \( x = 10 \), \( y = 20 \). Check: \( 50(10)+150(20)=500 + 3000 = 3500 \leq 4000 \). Wait, but problem says "overloaded"? Wait, maybe inequality for overloaded is \( 50x + 150y > 4000 \). Let's recast: \( 50x + 150y > 4000 \) → \( x + 3y > 80 \). Try \( x = 25 \), \( y = 20 \): \( 25 + 60 = 85 > 80 \). So \( (25,20) \): 25 children, 20 adults. \( 50*25 + 150*20 = 1250 + 3000 = 4250 > 4000 \), overloaded.

Step3: Verify Graph

The graph's shaded region (yellow) is above the line (since overloaded is above capacity). So ordered pairs in yellow satisfy \( 50x + 150y > 4000 \).

Answer:

The point \((25, 20)\) satisfies the inequality. The coordinates represent the fact that when 25 children and 20 adults are in the elevator, the elevator is overloaded. (Note: Other valid points like \((10, 30)\) (5010 + 15030 = 500 + 4500 = 5000 > 4000) also work, but \((25,20)\) is an example.)