Variation

Setup

100

x varies directly with y

x=ky

200

x varies jointly with y and z

x=kyz

300

x varies inversely with y

x=k/y

400

x varies jointly as y and z and inversely as m

x=kyz/m

500

z varies directly as x and the square of y

z=kx(y^2)

Direct

100

x varies directly with y, find x when y=2 if x=8 and y=4

x=8

200

y varies directly with z find y when z=5, if y=4 and z=20

y=1

300

x varies directly as y, find y when x=8, if x=12 and y=3

y=4

400

x varies directly with t find t when x=4, if t=8 and x=16

t=2

500

x varies directly with z squared, find x when and z=4, if x=12 and z=6

x=48

Joint

100

x varies jointly with y and z, find x when y=2 z=6, if x=20, y=2 and z=2

x=60

200

x varies jointly with y z and t, find x when y=2,z=5,t=2, if x=36, y=2,x=2, and t=3

x=120

300

x varies jointly with y and z, find x when z=2 and y=4, if x=45, z=3 and y=3

x=24

400

x varies jointly with y and z, find z when x=8 and y=2, if x=48, y=2 and z=2

z=1/3

500

y varies jointly with m and g squared, find m when when y=60 and g=2, if y=45, m=1 and g=3

m=3

Inverse

100

x varies inversely with y find x when y=2 if x=2 and y=6

x=6

200

x varies directly with y and inversely with z, find x when y=5 and z=10, if x=5 z=4 and y=2

x=5

300

x varies inversely with z find z  when x=8 if z=4 and x=4

z=2

400

x varies inversely with y find y when x=6 if x=4 and y=3

y=2

500

y varies directly with x squared and inversely with y, find y if x=4 and z=8, if x=8, y =16 and z=12

y=6