A farmer wants to know how many horses and chickens are on the farm. She counted 82 feet and 26 animals. How many of each is there?

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A farmer wants to know how many horses and chickens are on the farm. She counted 82 feet and 26 animals. How many of each is there?

From the problem, you know that there is a total of 82 feet and 26 animals. There are 4 feet per horse and 2 feet per chicken, which would equal to a total of 82 feet when combined.

If x represents total number of horses and y represents total number of chickens then the equations to the problem would appear like this:

x+y=26 (26 being total number of chickens and horses when combined)
4x+2y=82 (we are multiplying x by 4 because each horse has 4 legs and multiplying y by two because each chicken has 2 legs. We equal it to 82 because that represents the total number of legs when combined)

Now it is a system of equations which can be solved using substitution:
x+y=26
-y -y
x=26-y (now substitute the answer for x of the second equation)

4x+2y=82

4(26-y)+2y=82

104-4y+2y=82

104-2y=82
-104 -104

-2y= -22 (divide by -2 on both sides)
y= 11 (total number of chickens. Then substitute 11 for y in the equation you started with)

x+y=26

x+11=26
-11 -11

x= 15 (total number of horses)

There is a total of 15 horses and 11 chickens on the farm. (to check, plug in both numbers to the equations to see if they work)