the farmhouse shelters 11 animals. some are geese and some are cows. there are 38 legs in all. how many of each animal are there?

Question

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Answer 1

Let x = number of geese

     y = number of cows

 

The number of legs is:

    2x + 4y = 38                ["38 legs in all"]

 

The number of animals is:

     x + y = 11                ["11 animals"]

 

The math (use either elimination or substitution; let's use elimination]:

 

   2x + 4y = 38

   2x + 2y = 22      [2*second equation]

-------------------    [elimination; subtract equations]

          2y  = 16

            y  =  8

 

   x + y = 11     [second equation again]

         y =  8      [solution just found]

 --------------     [elimination; subtract equations]

   x       = 3

 

3 geese and 8 cows (11 animals with 2*3+4*8=38 legs total]