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
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
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
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