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

Question

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

Answer 1

Two equations:

 

b=#of birds

r=#of rabbits

 

b+r=170 (both animals have one head)

2b+4r=402 (number of legs)

 

 

Answer 2

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.

Answer 3

Let's say there are r rabbits and b 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 r rabbits have a total of 4 * r = 4r  legs

 

Each bird has 2 legs, so b birds have a total of 2b legs

 

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