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word problem trying to set up a formula to find the answer

AS i looked out into the park I saw rabbits and birds. I count 170 heads and 402 feet. How many rabbits and how many birds are there? (animals are normal, rabbit has 1 head-4feet and birds have 1 head-2 feet)
Need to set up as a equation and slove

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Valerie C. | ADHD/ADD Executive Function TutorADHD/ADD Executive Function Tutor
Two equations:
b=#of birds
r=#of rabbits
b+r=170 (both animals have one head)
2b+4r=402 (number of legs)


Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)
Mental math: Assuming all are birds, you would have 170*2 = 340 feet. Now you have 402-340 = 62 extra feet. That means you have 62/2 = 31 rabbits because switching each bird to a rabbit you get two extra feet.
Answer: 31 rabbits and 170-31 = 139 birds.


Thanks so much for putting it into simple form for me. Sometimes we try to over think the obvious.Appreciate your help
Imtiazur S. | Tutor with masters degree and experience teaching CalculusTutor with masters degree and experience...
4.9 4.9 (343 lesson ratings) (343)
Let's say there are rabbits and birds
Since there are 170 heads and each bird and rabbit has one head, we can write the following first equation
r + b = 170  ----------------let's call this equation 1
Also, each rabbit has 4 legs, so rabbits have a total of 4 * = 4 legs
Each bird has 2 legs, so b birds have a total of 2legs
The total number of legs from the above accounting is 4r + 2b legs
But we know that the total legs observed are 402.  With this information we form the second equation below
4r + 2b = 402 ----------------let's call this equation 2
solving for the variables using equations 1 and 2, we get our solution of 31 rabbits and 139 birds