Question 981073


The fact that  "the variable  Z  is directly proportional to  X,  and inversely proportional to  Y"  (which is the given condition)  means that


{{{Z}}} = {{{k*(X/Y)}}},


where  {{{k}}} = const  (is a constant value).  If you substitute  {{{X=3}}},  {{{Y=6}}}  and  {{{Z=9.5}}}  into this formula,  you will get


{{{9.5}}} = {{{k*(3/6)}}} = {{{k/2}}}.


Hence,  {{{k}}} = {{{9.5*2}}} = {{{19}}}.


Thus our formula for  {{{Z}}}  is


{{{Z}}} = {{{19*(X/Y)}}}.


Now,  if you substitute  {{{X=8}}}  and  {{{Y=12}}}  into the last formula,  you will get


{{{Z}}} = {{{19*(8/12)}}} = {{{(19*8)/12}}} = {{{12.667}}} (approximately).


It is the answer to your question.