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?

horses-and-chickens

#1

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?

Answer:

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)