### All PSAT 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:**

8

2

6

1

4

**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

varies inversely as the cube of .

If when , then evaluate when . (Nearest tenth)

**Possible Answers:**

**Correct answer:**

If varies inversely as the cube of , then, if are the initial values of the variables and are the final values,

Substitute and find :

This rounds to 2.3.

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

varies inversely as the cube root of .

If when , then evaluate when . (Nearest tenth)

**Possible Answers:**

**Correct answer:**

If varies inversely as the cube root of , then, if are the initial values of the variables and are the final values,

Substitute and find :

### Example Question #3 : How To Find Inverse Variation

Find the inverse of

**Possible Answers:**

**Correct answer:**

To find the inverse we first switch the x and y variables

Now we add 4 to each side

From here to isolate y we need to multiply each side by 2

By distributing the 2 we get our final solution:

### Example Question #4 : How To Find Inverse Variation

varies inversely as the square of .

If when , then evaluate when . (Nearest tenth)

**Possible Answers:**

**Correct answer:**

If varies inversely as the square of , then, if are the initial values of the variables and are the final values,

.

Substitute and find :

This rounds to 3.5.

### Example Question #5 : How To Find Inverse Variation

varies inversely with the square root of .

If when , then evaluate when . (Nearest tenth)

**Possible Answers:**

**Correct answer:**

If varies inversely with the square root of , then, if are the initial values of the variables and are the final values,

.

Substitute and find :

### Example Question #6 : How To Find Inverse Variation

Find the inverse of .

**Possible Answers:**

**Correct answer:**

To find the inverse of a function we need to first switch the and . Therefore, becomes

We now solve for y by subtracting 1 from each side

From here we divide both sides by 2 which results in

### Example Question #7 : How To Find Inverse Variation

Find the inverse of .

**Possible Answers:**

**Correct answer:**

To find the inverse we first switch the variables then solve for y.

Then we subtract from each side

Now we divide by to get our final answer. When we divide by we are left with . When we divide by we are left with . Thus resulting in:

### Example Question #3 : Algebraic Fractions

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 : How To Find Inverse Variation

Find the inverse equation of .

**Possible Answers:**

**Correct answer:**

1. Switch the and variables in the above equation.

2. Solve for :

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