Question

If z varies in inverse proportion to w, and z=3 when w=8. How do you find the inverse variation equation and use it to calculate z when w=2?

Answer 1

Hint: The statement: z varies inversely as w means that when w increases, z decreases by the same factor. To solve the inverse variation questions, we must first know the equation $z = \dfrac{k}{w}$ , in which we must find the value of k by considering the values of w and z, and then find the inverse variation of z when w=2.

Complete step-by-step solution:
We have given that z varies inversely with w,
We have z=3 when w=8
We know that according to relation
$z = \dfrac{k}{w}$............................(1)
where k is the relation constant
we will substitute the value of z and w in the equation 1 and find the value of k
$z = \dfrac{k}{w}$
$3 = \dfrac{k}{8}$
Multiplying the both side by 8, we get
$k = 24$
Now we have to find the value of z when w=2.
We know the value of relation constant k.
We will substitute the value w=2 and k=24 in equation 1
$z = \dfrac{k}{w}$
We have put the value of w and k,
$z = \dfrac{{24}}{2}$
$z = 12$

Note: Inverse variation equations are solved with the equation $z = 12$ ; carefully read the problem to see if there are any other changes in the inverse variation equation, such as squares, cubes, or square roots. Find the value of k, also known as the constant of variation or the constant of proportionality, using the information provided in the problem.