The quantities x, y and z are such that y proportional to  x and z proportional to  y. If y =30 when x = 5 and z = 28 when y = 20 , find the relationship between x and z.​
   

Dear Student,

Please find below the solution to the asked query:

Given :  y proportional to  x , So 

y $\propto$ x  ,

y  = k₁ x                              --- ( 1 )  , Here k₁ is proportional coefficient

Also given : If y =30 when x = 5 , So

30 = k₁ ( 5 ) ,

k₁ = 6 

And z proportional to  y.

z $\propto$ y  ,

z  = k₂ y                              --- ( 2 )  , Here k₂ is proportional coefficient

Also given : If  z = 28 when y = 20 , So

28 = k₂ ( 20) ,

k₂ = 1.4

Now we substitute value from equation 1 to equation 2 and get :

z  = k₂ ( k₁ x )

Now we substitute values of k₁ and k₂ and get :

z = ( 1.4)(6) x ,

z = 8.4 x                                                                              ( Ans )


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