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

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

Tutors, please sign in to answer this question.

Washington, CT

Two equations:

b=#of birds

r=#of rabbits

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

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

Scottsdale, AZ

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

Olathe, KS

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.

Amaan M.

Math/Economics Teacher

New York, NY

5.0
(68 ratings)

Romina A.

Knowledgeable tutor in Spanish, Biology, Anatomy & Physiology and Math

Harrison, NJ

5.0
(169 ratings)

Mary F.

Highly Qualified Math Teacher, Kaplan Trained

Bronxville, NY

5.0
(55 ratings)

- Algebra 4715
- Algebra 1 3844
- Algebra 2 3233
- Algebra Help 946
- Word Problem 4836
- Math 9007
- Math Help 5020
- Math Word Problem 4049
- Algebra 2 Question 481
- Word Problem Help 1075

## Comments