Question

Determine the equation of joint variation. Then solve for the missing value.

x varies directly with y and z.
x = 400 when y = 8 and z = 10.
Find x when y = 10 and z = 12.

Answer 1

If
"x varies directly with y and z",
that means
x=kyz, where k is a constant.

Since
x = 400 when y = 8 and z = 10
or
400=k(8)(10),
we can readily solve for k=5.

Hence solve for x when
when y = 10 and z = 12
(hint: k=5)

Answer 2

Determine the equation of combined variation. Then solve for the missing value.

x varies directly with y and inversely with z.
x = 5 when y = 10 and z = 5.
Find x when y = 20 and z = 10.