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Word Problems: Inverse Variation

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Word Problems: Inverse Variation

Study Guide

Key Definition

Inverse variation describes a relationship where as one variable increases, the other decreases. Expressed by $x · y = k$.

Important Notes

Inverse variation can be written as $y = \frac{k}{x}$
In these relationships, $k$ is a nonzero constant
If $x$ increases, $y$ decreases and vice versa
Always check for non-zero values of $x$ and $y$
Used to solve real-world problems involving rates or ratios

Mathematical Notation

$\times$ represents multiplication

$\frac{a}{b}$ represents a fraction

$y = \frac{k}{x}$ shows inverse variation

Remember to use proper notation when solving problems

Why It Works

Inverse variation works because it maintains a constant product $x · y = k$, showing the relationship between two inversely related quantities.

Remember

In inverse variation problems, the product of the variables is constant: $x · y = k$

Quick Reference

Inverse Variation Formula:$y = \frac{k}{x}$

Understanding Word Problems: Inverse Variation

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

In inverse variation, one quantity increases as the other decreases, following $y = \frac{k}{x}$. For example, if x doubles, y halves.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

If $xy = 24$ and $x = 6$, what is $y$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

A car travels a fixed distance. If the speed is $60 \, \text{km/h}$ and takes $2$ hours, how long will it take at $80 \, \text{km/h}$?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

If $x · y = 50$ and $x$ is increased to $10$, what happens to $y$?

Challenge Quiz

Single Choice Quiz

Advanced

The pressure $P$ and volume $V$ of gas are inversely proportional. If $P = 30$ and $V = 240$, find $P$ when $V = 160$.

Recap

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