Question

Suppose that y varies jointly with w and x and inversely with z and y = 400 when w = 10, x = 25, and z = 5. Write the equation that models the relationship.

Answer 1

`y =8 \cdot (wx)/(z)`

Explanation:

Joint variation says that:

If y varies jointly with x and inversely with z

i.e,

`y \propto x`

`y \propto (1)/(z)`

then the equation is in the form of :

`y = k(x)/(z)` where, k is the constant of variation.

As per the statement:

Suppose that y varies jointly with w and x and inversely with z

by definition of joint variation we have;

`y = k(wx)/(z)` ......[1]

It is given that: y = 400 when w = 10 , x = 25 and z = 5

Substitute in [1] we have;

`400 = k \cdot (10 \cdot 25)/(5)`

Simplify:

`400 = 50k`

Divide both sides by 50 we have;

8 = k

or

k = 8

⇒
`y =8 \cdot (wx)/(z)`

Therefore, the equation that models the relationship is,
`y =8 \cdot (wx)/(z)`