Given:
x is directly proportional to y and inversely proportional to z.
x= 15 when y = 10 and z= 4.
To find:
The equation that connecting x, y and z.
Solution:
It is given that, x is directly proportional to y and inversely proportional to z.
[tex]x\propto \dfrac{y}{z}[/tex]
[tex]x=\dfrac{ky}{z}[/tex] ...(i)
Where, k is the constant of proportionality.
We have, x= 15 when y = 10 and z= 4.
[tex]15=\dfrac{k(10)}{4}[/tex]
[tex]15\times 4=10k[/tex]
[tex]60=10k[/tex]
Divide both sides by 10.
[tex]\dfrac{60}{10}=k[/tex]
[tex]6=k[/tex]
Putting k=6 in (i), we get
[tex]x=\dfrac{6y}{z}[/tex]
Therefore, the required equation is [tex]x=\dfrac{6y}{z}[/tex].
