Many elevators have a capacity of 2000 pounds. a. If a child...

Many elevators have a capacity of 2000 pounds. a. If a child averages 50 pounds and an adult 150 pounds, write an inequality that describes when $x$ children and $y$ adults will cause the elevator to be overloaded. b. Graph the inequality. Because $x$ and $y$ must be positive, limit the graph to quadrant I only. c. Select an ordered pair satisfying the inequality. What are its coordinates and what do they represent in this situation?

Many elevators have a capacity of 2000 pounds.
a. If a child averages 50 pounds and an adult 150 pounds, write an inequality that describes when $x$ children and $y$ adults will cause the elevator to be overloaded.
b. Graph the inequality. Because $x$ and $y$ must be positive, limit the graph to quadrant I only.
c. Select an ordered pair satisfying the inequality. What are its coordinates and what do they represent in this situation?

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Key Concepts

Linear Inequalities

A linear inequality involves a linear expression in one or more variables with an inequality sign, representing a range of possible solutions rather than a single value. In modeling scenarios, these inequalities help determine the conditions under which certain combinations of variables satisfy given resource limitations or constraints.

Graphing Linear Inequalities

Graphing a linear inequality involves plotting the boundary line associated with the equality and then shading the appropriate region based on the inequality symbol. This visualization helps in identifying all the potential solution sets, especially in two-variable contexts, and is often limited to the first quadrant when the variables represent quantities that cannot be negative.

Interpreting Ordered Pairs in Context

Ordered pairs in the context of inequalities represent specific combinations of values that satisfy the given inequality. Each coordinate in the pair corresponds to a value of one of the variables, and together they provide a tangible example of a possible scenario within the defined constraints.

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