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# word problems and turning them into algebraic equation to slove

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

### 2 Answers by Expert Tutors

Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
3.0 3.0 (1 lesson ratings) (1)
1
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
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

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

thank you for your help. Appreciate the great explanation!
PING W. | Experienced Bilingual Accounting Tutor - PingExperienced Bilingual Accounting Tutor -...
5.0 5.0 (59 lesson ratings) (59)
1
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

p=10        plug in (3) :   c=d-4
c=d-4       plug in (1) :   10 + (d -4) +d =30
6 +2d=30
d=12
d=12        plug in (3)     10+c=12+6
c=8