### All ACT Math Resources

## Example Questions

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

varies inversely with . When , . What does equal when ?

**Possible Answers:**

**Correct answer:**

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

2. Solve for when in the above equation:

### Example Question #8 : Direct And Inverse Variation

If , what is the value of ?

**Possible Answers:**

**Correct answer:**

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 #9 : 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?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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

For our data, this means:

You merely need to solve for :

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