Inverse variation. Please help me understand this pre-test question

Question

a)if X varies directly as y and inversely as the square of z, and x=16 when y=4 and z=4 a)write the equation of variation b)find x when y=8 and z=8 

 

 

Answer 1

Generic forms for direct and inverse variations:

x varies directly as y:  x = ky

x varies inversely with y:  x =k/y

 

If x varies directly with y and inversely with square of z then:

x = ky/z²   where k is the constant of proportion

 

x = 16, y = 4, z =4 ... plug in and solve for k

 

16 = 4k/4²

16 = 4k/16

16 = k/4

k = 64

Your equation is:  x = 64y/z²

 

Now just plug in 8 for y and 8 for z and solve for x

x = 64(8)/8²

x = 8