Question

at old oak farm, there are chicken and horses. there are 120 legs and 48 heads altogether. how many horses and how many chickens are there?

Answer 1

Explanation:

We must use system of equations:

horses = h chickens = c

horses have 4 legs & chickens have 2 and there are 120 legs total so to set up the first part of the equation...

4h + 2c = 120

They both have only 1 head each and there are 48 heads total so to set up the second part of the equation...

h + c = 48

Now we combine the equations and solve:

4h + 2c = 120

h + c = 48

Now we solve...

4h + 2c = 120

h = 48 - c (subtract c on both sides to single out h)

--------------------

4(48 - c) + 2c = 120

192 - 4c + 2c = 120

-192 -192

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-2c = -72 (divide both sides by -2)

c = 36

Now we go back and find the value of h...

h = 48 - c

h = 48 - 36

h = 12

So there are 36 chickens & 12 horses!