Tara looks out into the park and sees pigs. chickens and ducks. She counts 30 heads and 80 feet. The sum of the number of pigs and chickens is 6 more than the number of ducks. ( all animals have normal amount ofheads and feet)

HOW MANY pigs, chickens and ducks are out there? Set up equation and solve

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Hi Nancy;

FIRST EQUATION...P+C+D=30

SECOND EQUATION...P+C=D+6

4P+2C+2D=80

Let's divide both sides by 2...

THIRD EQUATION...2P+C+D=40

Let's begin with the second equation..

P+C=D+6

This is also...

P+C-D=6

Let's add the first equation and second equation....

P+C-D=6

+(P+C+D=30)

2P+2C=36

Let's divide both sides by 2...

P+C=18--------we will use this again below...

The first equation was...

P+C+D=30

Let's substitute P+C with 18...

18+D=30

Let's subtract 18 from both sides...

D=12

Let's return to the third equation...

2P+C+D=40

2P+C+12=40

Let's subtract 12 from both sides...

2P+C=28

Let's subtract formulas...

2P+C=28

-(P+C=18)------from above

P=10

Let's return to the first equation...

P+C+D=30

10+C+12=30

C+22=30

C=8

Let's double check this with the third equation...

2P+C+D=40

2(10)+8+12=40

20+8+12=40

40=40

Let set p for pigs, c for chickens, and d for ducks

(1) p+c+d= 30 (She counts 30 heads, each animal has one head)

(2) 4p + 2c + 2d = 80 (each pig has 4 feet. each chicken and duck has 2 feet )

(3) p + c = d + 6

solve the three equations : (2) - (1) *2 : 4p + 2c + 2d - (2p+2c+2d) = 80- 30*2

2p = 20

p=10 plug in (3) : c=d-4

c=d-4 plug in (1) : 10 + (d -4) +d =30

6 +2d=30

d=12 plug in (3) 10+c=12+6

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