# SAT Math : How to find inverse variation

## Example Questions

### Example Question #1 : How To Find Inverse Variation

A school's tornado shelter has enough food to last 20 children for 6 days. If 24 children ended up taking shelter together, for how many fewer days will the food last?

4

8

1

6

2

1

Explanation:

Because the number of days goes down as the number of children goes up, this problem type is inverse variation. We can solve this problem by the following steps:

20*6=24*x

120=24x

x=120/24

x=5

In this equation, x represents the total number of days that can be weathered by 24 students. This is down from the 6 days that 20 students could take shelter together. So the difference is 1 day less.

### Example Question #1 : How To Find Inverse Variation

Find the inverse equation of:

Explanation:

To solve for an inverse, we switch x and y and solve for y. Doing so yields:

### Example Question #2 : How To Find Inverse Variation

Find the inverse equation of  .

Explanation:

1. Switch the  and  variables in the above equation.

2. Solve for :

### Example Question #1 : How To Find Inverse Variation

When ,  .

When .

If  varies inversely with , what is the value of  when ?

Explanation:

If  varies inversely with .

1. Using any of the two  combinations given, solve for :

Using :

2. Use your new equation  and solve when :

### Example Question #2 : How To Find Inverse Variation

 x y

If  varies inversely with , what is the value of ?

Explanation:

An inverse variation is a function in the form:  or , where  is not equal to 0.

Substitute each  in .

Therefore, the constant of variation, , must equal 24. If  varies inversely as must equal 24. Solve for .