Question

A farmer saw some chickens and pigs in a field. He counted 51 heads and 172 legs. Determine

exactly how many chickens and pigs he saw.
How many chickens?
How many pigs?

Answer 1

Answers:

16 chickens

35 pigs

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Step-by-step explanation:

x = number of chickens

y = number of pigs

There are 51 heads, so x+y = 51 which solves to y = 51-x

2x = number of legs just from the chickens (2 legs per chicken)

4y = number of legs just from the pigs (4 legs per pig)

2x+4y = 172 legs total

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Plug in y = 51-x and solve for x.

2x+4y = 172

2x+4(51-x) = 172

2x+204-4x = 172

-2x+204 = 172

-2x = 172-204

-2x = -32

x = -32/(-2)

x = 16

Now use this to find y

y = 51-x

y = 51-16

y = 35

Since x = 16 and y = 35, this means there are 16 chickens and 35 pigs.

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Check:

x+y = 16+35 = 51 which works

2x+4y = 2*16+4*35 = 172 and that also works.

Both equations are confirmed.