Question

The variable z is directly proportional to x, and inversely proportional to y. When x is 9 and y is 6, z has the value 19.5. What is the value of z when x= 14, and y= 11

Answer 1

Given that, the variable z is directly proportional to x, and inversely proportional to y.

So, we can set up an equation as following:

`z= k (x)/(y)` Where k = constant of variation.

Another information given in the problem is, when x is 9 and y is 6, z has the value 19.5.

So, x = 9, y = 6 and z = 19.5.

Let's plug in these values in the above equation. So,

`19.5= k (9)/(6)`

19.5 = k* 1.5

`(19.5)/(1.5) =k` Divided each sides by 1.5 to isolate k.

So, k = 13.

Hence, the equation will be
`z= 13 (x)/(y)`.

Now we need to find the value of z when x= 14, and y= 11 . Therefore,

`z= 13*(14)/(11)`

`z= (182)/(11)`

So, z= 16.5 (Rounded to tenth).

Hope this helps you!