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A farmer saw some chickens and pigs in a field. He counted 60 heads and 176 legs. How many chickens and how many pigs did the farmer see ?

Respuesta :

He saw 32 chickens and 28 pigs.

Let p be the number of pigs and c be the number of chickens.

Each pig has 1 head and each chicken has 1 head; this gives us the equation
1p + 1c = 60 or
p + c = 60

Each pig has 4 legs and each chicken has 2 legs; this gives us the equation
4p + 2c = 176

In the first equation, we will isolate c by subtracting p from both sides:
p + c - p = 60 - p
c = 60 - p

We will substitute this into the second equation:
4p + 2(60 - p) = 176

Using the distributive property, 
4p + 2*60 - 2*p = 176
4p + 120 - 2p = 176

Combining like terms,
2p + 120 = 176

Subtract 120 from each side:
2p + 120 - 120 = 176 - 120
2p = 56

Divide both sides by 2:
2p/2 = 56/2
p = 28

There are 28 pigs.

Substitute this into the first equation:
p + c = 60 
28 + c = 60

Subtract 28 from each side:
28 + c - 28 = 60 - 28
p = 32
abidemiokin

There are 32 chickens and 28 pigs in the field if a farmer saw some chickens and pigs in a field and counted 60 heads and 176 legs.

Let the number of chickens the farmer saw be x

Let the number of pigs the farmer saw be y

If a farmer saw some chickens and pigs in a field, then;

x + y = 60 (since both animals have one head)

Note that the chickens have 2 legs and the pigs have 4 legs, if the farmer saw 176 legs, hence;

2x + 4y = 176

Solve both equations simultaneously;

x + y = 60 .......................... 1 * 2

2x + 4y = 176 ....................... 2 * 1

__________________________________

2x + 2y = 120

2x + 4y = 176

Subtract

2y - 4y = 120 - 176

-2y = -56

y = 28

Recall that x + y = 60

x = 60 - y

x = 60 - 28

x = 32

This means that there are 32 chickens and 28 pigs in the field

Learn more here: https://brainly.com/question/15165519

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