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

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3 Answers

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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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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