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:

$z= k \frac{x}{y}$ 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,

$19.5= k \frac{9}{6}$

19.5 = k* 1.5

$\frac{19.5}{1.5} =k$ Divided each sides by 1.5 to isolate k.

So, k = 13.

Hence, the equation will be $z= 13 \frac{x}{y}$.

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

$z= 13*\frac{14}{11}$

$z= \frac{182}{11}$

So, z= 16.5 (Rounded to tenth).

Hope this helps you!