### All SAT Math Resources

## 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?

**Possible Answers:**

2

8

4

6

1

**Correct answer:**

1

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:

**Possible Answers:**

**Correct answer:**

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

### Example Question #2 : Algebraic Fractions

Find the inverse equation of .

**Possible Answers:**

**Correct answer:**

1. Switch the and variables in the above equation.

2. Solve for :

### Example Question #2 : Algebraic Fractions

When , .

When , .

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

**Possible Answers:**

**Correct answer:**

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 #1 : Algebraic Fractions

x |
y |

If varies inversely with , what is the value of ?

**Possible Answers:**

**Correct answer:**

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 .