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 · 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#

Related questions
Impact of this question
42520 views around the world
You can reuse this answer
Creative Commons License