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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
1
Two equations:
 
b=#of birds
r=#of rabbits
 
b+r=170 (both animals have one head)
2b+4r=402 (number of legs)
 
 

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Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)
1
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.

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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)
1
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
 
 
 

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