In order to solve for, first set up the variation equation forand:

whereis the constant of variation. Theterm varies indirectly withand is therefore in the denominator.

Next, we solve forbased on the initial values of the variables:

Now that we have the value of, we can solve forin the second scenario:

The problem follows the formula

where P is the number of slices you get, n is the number of people, and k is the constant of variation.

Setting P=3 and n = 16 yields k=48.

Now we substitute 12 in for n and solve for P

Therefore with 12 people, you get 4 slices.

The problem follows the formula

where R is the number of raffle tickets you get, n is the number of people, and k is the constant of variation.

Setting R=20 and n = 150 yields k=3000.

Plugging in 100 for n and solving for R you get:

The answer R is 30 tickets.

The problem follows the formula

where B is the budget per committee, n is the number of committees, and k is the constant of variation.

Setting B=500 and n = 4 yields k=2000.

Now using the following equation we can plug in our n of 2 and solve for B.

The answer of B is $1000.

The problem follows the formula

where H is the number of hours to complete the job, n is the number of people hired, and k is the constant of variation.

Setting H=6 and n = 8 yields k=48.

Therefore using the following equation we can plug 16 in for n and solve for H.

Therefore H is 3 hours.

varies inversely with, so the variation equation can be written as:

can be solved for, using the first scenario:

Using this value for= 30 and= 90, we can solve for:

From the first sentence, we can write the equation of variation as:

We can then check each of the possible answer choices by substituting the values into the variation equation with the values given forand．

Therefore the equation is true ifand

Therefore the equation is true ifand

Therefore the equation is true ifand

The correct answer choice is then "All of these answers are correct"

From the relationship of,, and; the equation of variation can be written as:

Using the values given in the first scenario, we can solve for k:

Using the value of k and the values of y and z, we can solve for x:

First, we can create an equation of variation from the the relationships given:

Next, we substitute the values given in the first scenario to solve for:

Using the value for, we can now use the second values forandto solve for:

From the relationship given, we can set up the variation equation

Using the first relationship, we can then solve for

Now using the values from the second relationship, we can solve for x