# ACT Math : How to use the inverse variation formula

## Example Questions

### Example Question #5 : Direct And Inverse Variation

varies inversely with . When , . What does  equal when

Explanation:

1. Use the given values of  and  to solve for :

2. Solve for  when  in the above equation:

### Example Question #6 : Direct And Inverse Variation

If , what is the value of ?

Explanation:

To solve this algebraic equation, subtract  from both sides, and then subtract  from both sides.

We end up with the equation , for which the solution is:

### Example Question #1 : Direct And Inverse Variation

In a given set of experiments, the values of two variables are always inversely proportional. If in the first experiment the first variable was  and the second was , what could you expect the second variable to be if the first is  in a later experiment?

Explanation:

Recall that inverse variation means that when one variable increases, the other decreases. This gives you the following equation:

Now, for our data, we know:

You merely have to solve for :

Divide by :

### Example Question #1 : Direct And Inverse Variation

Throughout a party, the number of joyful non-philosophers in a room is always inversely proportional to the number of philosophers in the room. The room begins with  people,  of whom are philosophers. Later in the day, there are  philosophers in the room. How many joyful non-philosophers are at the party at the later time?