There are 13 animals in the barn. Some are chickens and some are pigs. There are 40 legs in all. How many of each animal are there?

Answer 1

Let C = the number of Chickens

Let P = the number of Pigs

EQUATION 1 IS FOR THE NUMBER OF ANIMALS

C + P = 13

EQUATION 2 IS FOR THE NUMBER OF LEGS

2C + 4P = 40 (chickens have 2 legs, and pigs have 4 legs.)

SOLVING TWO SIMULTANEOUS LINEAR EQUATIONS

C + P = 13

2C + 4P = 40

3 METHODS OF SOLVING: GRAPH BOTH LINES, SUBSTITUTION, AND ELIMINATION.

LET'S ELIMINATE THE C's OR CHICKENS BY MULTIPLYING THE TOP EQUATION BY -2.

-2C - 2P = -26

2C + 4P = 40

============= ADD THESE TWO LINEAR EQUATIONS

2P = 14

P = 7 THERE ARE 7 PIGS, AND THEY ACCOUNT FOR 28 LEGS

TOP EQUATION: C + P = 13

C + 7 = 13

C = 6 THERE ARE 6 CHICKENS, AND THEY ACCOUNT FOR 12 LEGS

6 CHICKENS

7 PIGS