Given:
z varies directly with x and inversely with y, when x = 2, y = 5, and z = 10.
To find:
The value of z when x=3 and y=15.
Solution:
It is given that z varies directly with x and inversely with y. So,
[tex]z\propto \dfrac{x}{y}[/tex]
[tex]z=k\cdot \dfrac{x}{y}[/tex] ...(i)
Where k is the constant of proportionality.
We have x = 2, y = 5, and z = 10. After substituting these values, we get
[tex]10=k\cdot \dfrac{2}{5}[/tex]
[tex]10\times 5=2k[/tex]
[tex]\dfrac{50}{2}=k[/tex]
[tex]25=k[/tex]
The value of k is 25. After substituting k=25 in (i), we get
[tex]z=25\cdot \dfrac{x}{y}[/tex] ...(ii)
We need to find the value of z when x=3 and y=15. Substituting x=3 and y=15 in (ii), we get
[tex]z=25\cdot \dfrac{3}{15}[/tex]
[tex]z=25\cdot \dfrac{1}{5}[/tex]
[tex]z=5[/tex]
Therefore, the value of z is 5 when x = 3 and y = 15.
