a Student sees rabbits, ducks and birds in the park. she counts 22 heads and 52 feet. students know that the number of birds is 2 more than the sum of the rabbits and ducks. how many of each animal is there. ( all animals are normal )?

Hi Nancy;

*a Student sees rabbits, ducks and birds in the park. she counts 22 heads and 52 feet. students know that the number of birds is 2 more than the sum of the rabbits and ducks. how many of each animal is there. ( all animals are normal )?*

22=R+B+D

B=R+D+2

52=4R+2B+2D

The last equation can also be...

26=2R+B+D

Let's consider the following equations...

26=2R+B+D

22= R+B+D

Let's subtract the second equation from the first...

4=R

22=R+B+D

Let's substitute B with R+D+2

22=R+(R+D+2)+D

22=2R+2D+2

Let's substitute R with 4...

22=[2(4)]+2D+2

22=8+2D+2

Let's combine like terms...

22=2D+10

Let's subtract 10 from both sides...

22-10=D+10-10

12=2D

Let's divide both sides by 2...

12/2=2D/2

6=D

22=R+B+D

22=4+B+6

22=B+10

12=B

4 Rabbits

6 Ducks

12 Birds

Let's check our work...

Does

4+6+12=22?

22=22--YES!

Does

4(4)+2(6)+2(12)=52?

16+12+24=52

52=52--YES!

Does

12=4+6+2

12=12--YES!

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