Suppose that y varies jointly with w and x and inversely with z and y=400 when w=10, x=25 and z=5. How do you write the equation that models the relationship?

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Answer 1 · 2016-04-05T16:33:11

#y=8xx((wxx x)/z)#

As #y# varies jointly with #w# and #x#, this means

#yprop(wxx x)# .......(A)

#y# varies inversely with #z# and this means

#ypropz# ...........(B)

Combining (A) and B), we have

#yprop(wxx x)/z# or #y=kxx((wxx x)/z)# .....(C)

As when #w=10#, #x=25# and #z=5#, #y=400#

Putting these in (C), we get #400=kxx((10xx25)/5)=50k#

Hence #k=400/5=80 and our model equation is

#y=8xx((wxx x)/z)#