the number of rabbits

Question

The number of rabbits vary inversely as the number of foxes and directly as the number of cabbages.  When there were 120 rabbits, there were 15 foxes and 300 cabbages. How many cabbages were there when there were 90 rabbits and 10 foxes?

Answer 1

Let r = number of rabbits

     f = number of foxes

     c = number of cabbages

 

Then, r = kc/f, for some costant, k

 

When f = 15 and c = 300, r = 120.

 

   So, 120 = 300k / 15

 

         120 = 20k

 

             k = 6

 

So, r = 6c/f

 

If r = 90 and f = 10, 90 = 6c / 10

 

                                c = 150