Yet another farm problem to set up and solve.....

Tina looks out into the barnyard and sees pigs, chickens and ducks. She counts 38 heads and 86 feet. Knowing that that the sum of the number of pigs and chickens is 2 more than the number of ducks. (all animals are normal-each has 1 head, etc) set up the using algebra equations and solve.

Tutors, sign in to answer this question.

Let p = the number of pigs, c = number of chickens, and d = number of ducks.

p+c = d+2 ......(1)

P+c+d = 38 ......(2), balance by the total number of heads

4p+2c+2d = 86, balance by the total number of legs

/2, 2p+c+d = 43 ......(3)

(3)-(2): p = 5

(2)-(1): d = 36-d => d = 18

c = 38-p-d = 38-18-5 = 15

Answer: There are 5 pigs, 15 chickens and 18 ducks.

Hi Nancy;

FIRST EQUATION...P+C+D=38

4P+2C+2D=86

SECOND EQUATION...2P+C+D=43

P+C=D+2

THIRD EQUATION...P+C-D=2

------------

SECOND EQUATION...2P+C+D=43

FIRST EQUATION...P+C+D=38

Let's subtract the first equation from the second...

P=5

SECOND EQUATION...2(5)+C+D=43

SECOND EQUATION...10+C+D=43

THIRD EQUATION...P+C-D=2

THIRD EQUATION...5+C-D=2

Let's add the second and third equations...

15+2C+0=45

Let's subtract 15 from both sides..

2C=30

Let's divide both sides by 2...

C=15

FIRST EQUATION...P+C+D=38

5+15+D=38

20+D=38

D=18

SECOND EQUATION...2P+C+D=43

2(5)+15+18=43

10+15+18=43

25+18=43

43=43

THIRD EQUATION..P+C-D=2

5+15-18=2

20-18=2

2=2

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.

Emma Z.

Master of Accounting graduate tutoring business

$8.75 per 15 min

View Profile >

Ashley T.

Math, English, ACT/SAT prep tutor.

$7.50 per 15 min

View Profile >

Emma M.

Duke Biomedical Engineer. I make the impossible probable! I like math.

$10 per 15 min

View Profile >