The variable z is inversely proportional to x. When x is 12, z has the value 0.5. What is the value of z when x= 18?

Answer 1

The key here is the phrase "inversely proportional"

When A is inversely proportional to B, you should automatically write A = k/B, where k is the constant you'll solve for with other useful information later on. So in your problem where it says,

"z is inversely proportional to x" that translates to z = k/x

Now with the information given "When x =12 and z = 0.5" you can use your equation z = k/x to solve for k.

z = k/x

0.5 = k/12 (multiply both sides by 12)

0.5(12) = k

k = 6

Thus your equation is now: z = 6/x

So if x = 18,

z = 6/18 = 1/3

The procedure always goes as follows:

1) Translate "inversely proportional" or "directly proportional"

2) Plug in values given to solve for k

3) Rewrite your equation with the value of k you just found

4) Find the missing variable.

Hope it helps.

Mr. K

Answer 2

If z is inversely proportionate to x, then it needs to be set up as such:

z = k / x where k is the constant of proportionality.

Given x=12 and z=0.5. We can find k.

z = k/x

0.5 = k / 12 we multiply both sides by 12

12(0.5) = k

6 = k

Now that we found k and we are given x=18, we can find z.

z = k/x

z = 6/18

z = 1/3

Answer 3

z=k/x (definition of inversely proportional)

.5=k/12

k=6

therefore, if x=18 then z=6/18=1/3 or .33

Answer 4

"Inversely proportional" means that a 2 times increase in the independent variable causes a 2 times decrease in the dependent variable. The general equation is:

z = k / x, where k is a constant.

Using the given point, we can find the value of k:

0.5 = k / 12

k = 6

So the equation is z = k / x

x = 18, z = 6/18 = 1/3