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)

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

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

Also, each rabbit has 4 legs, so **r **rabbits have a total of 4 * **r **= 4**r ** legs

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

The total number of legs from the above accounting is 4**r + 2**b legs

But we know that the total legs observed are 402. With this information we form the second equation below

4**r** + 2**b** = 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

Great explanation. Thanks for putting it simple terms to understand, appreciate your help on this word problem.

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