Question

If x varies jointly as y and z, and x = 8 when y = 4 and z = 9, find z when x = 16 and y = 6. 3

Answer 1

z = 12.7

Explanation:

x = kyz

Where K is the constant of proportionality. We will be finding this

When x = 8 y =4 z = 9

K = 8/4 x 9 = 8/36

K = 0.2

To find z, when x = 16 and y = 6.3

Z = x/ky = 16/ 0.2x6.3 = 12.7

Answer 2

Joint variation says that:

if
`x \propto y` and
`x \propto z`

then the equation is in the form of:

`x = kyz`, where, k is the constant of variation.

As per the statement:

If x varies jointly as y and z

then by definition we have;

`x=k(yz)` ......[1]

Solve for k;

when x = 8 , y=4 and z=9

then

Substitute these in [1] we have;

`8=k(4 \cdot 9)`

⇒
`8 = 36k`

Divide both sides by 36 we have;

`(8)/(3)=k`

Simplify:

`k = (2)/(9)`

⇒
`x = (2)/(9)yz`

to find z when x = 16 and y = 6

Substitute these value we have;

`16 = (2)/(9) \cdot 6 \cdot z`

⇒
`16 = (12)/(9)z`

Multiply both sides by 9 we have;

`144 = 12z`

Divide both sides by 12 we have;

12 = z

or

z = 12

Therefore, the value of z is, 12