If x varies directly as y and inversely as z and when y=7 and z=2, x=14, what is x when y=16 and z=4?

2 Answers
Shwetank Mauria ยท mimi
Jun 14, 2017

x=16

Explanation:

x varies directly as y and inversely as z means xpropy and xprop1/z i.e.

xpropy xx1/z

In other words x=kxxy/z where k is a constant

Since when y=7 and z=2, we have x=14, we have

14=kxx7/2 and k=14xx2/7=4

and hence x=4y/z

and when y=16 and z=4

z=4xx16/4=16

Jim G.
Jun 14, 2017

x=16

Explanation:

"the initial statement is " xpropy/z

"to convert to an equation multiply by k the constant of"
"variation"

rArrx=kxxy/z=(ky)/z

"to find k use the condition given for x,y and z"

x=14,y=7,z=2

x=(ky)/zrArrk=(xz)/y=(14xx2)/7=4

rArr"equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(x=(4y)/z)color(white)(2/2)|)))

"when " y=16" and " z=4

rArrx=(4xx16)/4=16

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