Answer:
- k = 5/7; y = 5vw/(7z)
- w = 18/5; y = 10vw/z
- y = 3/2; k = 96
- v = 5/6; k = 8
- y = 168/5; y = 6vw/z
Explanation:
As with other forms of direct and inverse variation, the "constant of variation" (k) is the constant multiplier in the equation. "Varies directly" means the independent variable is in the numerator. "Varies inversely" means the independent variable is in the denominator. The variation equation can be solved for missing values of constants or variables.
The equation for "varies directly with v and w, and inversely with z" means the equation is of the form ...
y = k·v·w/z
Then the values of v or w are ...
v = y·z/(k·w)
w = y·z/(k·v)
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a)
k = y·z/(v·w) = 5·24/(12·14) = 5/7; the equation is y = 5·v·w/(7·z)
b)
w = y·z/(k·v) = 18·8/(10·4) = 18/5; the equation is y = 10·v·w/z
c)
k = 3/2 (read from the equation); y = (3/2)v·w/z = 3·16·24/(2·6) = 96
d)
k = 8 (read from the equation); v = y·z/(k·w) = 20·2/(8·6) = 5/6
e)
y = k·v·w/z = 6·12·7/15 = 168/5; the equation is y = 6·v·w/z