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

Answer:

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;

$\frac{8}{3}=k$

Simplify:

$k = \frac{2}{9}$

⇒$x = \frac{2}{9}yz$

to find z when x = 16 and y = 6

Substitute these value we have;

$16 = \frac{2}{9} \cdot 6 \cdot z$

⇒$16 = \frac{12}{9}z$

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

Answer 2

Answer:

z = 12.7

Step-by-step 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