Writing an Inverse Variation Equation

Writing an Inverse Variation Equation

An inverse variation equation is an equation written in the form, y = k/x, where k represents the constant of proportionality. In this interactivity, you will learn how to write inverse variation equations and how to use them to solve practical problems. Click the player button to begin.

View a printable version of this interactivity.

 

 

Alternate Strategy

In the previous interactivity, you were presented one strategy to solve problems involving inverse variations. Below is a Self-Check that was included in the interactivity, along with an alternate strategy to determine the solution.

Problem: The amount of time needed to paint a room varies inversely with the number of painters working. If 3 painters completed a room in 75 minutes, how long would it have taken 5 painters to complete the same room?

Response: Given inverse variation {(x₁ ,y₁),(x₂, y₂)}, the following proportion is true: y₂/y₁= x₁/x₂. You can use this relationship to solve the practice problem.

3 painters completed a room in 75 minutes.

5 painters would complete the same room in ? minutes.

minutes/minutes

=

painters/painters

x/75

=

3/5

5 · x

=

75 · 3

Cross-multiply

5x

=

225

Simplify

x

=

45

Divide both sides by 5

Five painters would have completed the room in 45 minutes.

 

Writing an Inverse Variation Equation Review

Now that you have learned how to write an inverse equation, it is time to test your knowledge. This interactivity will help you review the information covered throughout this topic. Click the player button to get started.