A farmhouse shelters 11 animals. Some are sheep some of our ducks. Altogether there are 28 legs. How many of each animal are there?

Question

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Answer 1

First, we must realize that each sheep has 4 legs and each duck has 2 legs. Because we have 2 unknowns, the number of sheep and the number of ducks, we must have 2 equations to solve it.

Let's let X=# of sheep

            Y=# of ducks.

Equation 1: X+Y=11

Equation 2: 4X+2Y=28

We can use either the substitution method or the elimination method to solve. Let's use the substitution method. From Equation 1 we can rewrite it to show that X=11-Y. Putting this value in for X in Equation 2 we can solve Y:

               4X+2Y=28

               4(11-Y)+2y=28

               44-4Y+2Y=28

               44-2y=28

               44=28+2Y      add 2Y to both sides

               44-28=2Y       subtract 28 from both sides

               16=2Y

                 8=Y             divide both sides by 2

Putting this value of Y into Equation 1 we get:

               X+Y=11

               X+8=11

               X=11-8          subtract 8 from both sides

               X=3

Therefore, there are 3 sheep and 8 ducks.