math

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.

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  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)

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  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.

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