Question 981067


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  (a constant value).  If you substitute  {{{X=6}}},  {{{Y=6}}}  and  {{{Z=12}}}  into this formula,  you will get


{{{12}}} = {{{k*(1/1)}}} = {{{k}}}.


Hence,  {{{k}}} = {{{12}}}. 


Thus our formula for  {{{z}}}  is


{{{Z}}} = {{{12*(X/Y)}}}.


Now,  if you substitute  {{{X=13}}}  and  {{{Y=10}}}  into the last formula,  you will get


{{{Z}}} = {{{12*(13/10)}}} = {{{(12*13)/10}}} = {{{156/10}}} = {{{15.6}}}.


It is the answer to your question.