SOLUTION: 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

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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
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

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 
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%2Ay%2Fz

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

Substitute these values:

112 = k·4%2A8%2F0.2

112 = k·32%2F0.2

112 = k·160

Divide both sides by 112

7%2F10 = k

Now substitute 7%2F10 for k in the first equation:

w = k·x%2Ay%2Fz

w = 7%2F10·x%2Ay%2Fz

w = %287%2Ax%2Ay%29%2F%2810%2Az%29

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

Substitute those values

w = %287%2Ax%2Ay%29%2F%2810z%29

w = 7%2A8%2A10%2F%2810%2A4%29

w = 14

Edwin