Question 743536


w varies jointly as x and y and inversely as z. one set of values is w=112 x=4, y=8 and z= 0.2. Find w when x=8, y=10 and z=4

<pre>
For all proportion problems, start with this:

Varying           "directly" or product of "jointlys" or 1 if none 
quantity  = k · ----------------------------------------------------------
                inversely variable or product of "inverselys" or 1 if none

In this problem the varying quantity is w.
the "jointlys" are x and y.  We have one inversely,z.  So we have x·y 
on top and z on the bottom:

w = k·{{{x*y/z}}}

>>...one set of values is w=112 x=4, y=8 and z= 0.2...<<

Substitute these values:

112 = k·{{{4*8/0.2}}}

112 = k·{{{32/0.2}}}

112 = k·{{{160}}}

Divide both sides by 112

{{{7/10}}} = k

Now substitute {{{7/10}}} for k in the first equation:

w = k·{{{x*y/z}}}

w = {{{7/10}}}·{{{x*y/z}}}

w = {{{(7*x*y)/(10*z)}}}

>>...Find w when x=8, y=10 and z=4...<<

Substitute those values

w = {{{(7*x*y)/(10z)}}}

w = {{{7*8*10/(10*4)}}}

w = 14

Edwin</pre>