Math Help Please!

Question

A farmer was asked how many cows she has. The farmer replied, “Between the cows and the chicken, there are 25 eyes and 76 feet.” How many cows does she have? How many chickens does she have?

 

 

This is an elementary school question but has me stumped. It just doesn't make sense. 

Answer 1

As has been stated, in order to have 25 eyes one of the animals

has either 1 eye or 3... since cows and chickens each have 2 eyes

the total eyes must be divisible by 2...  Still, since your problem

is stated as such, let's go with it...

 

Let x = # chickens

Let y = # cows

 

2x + 4y = 76    2 feet per chicken, 4 per cow

2x + 2y = 25    assuming all have 2 eyes

 

Subtract the 2nd equation from the 1st

 

2y = 51

y = 51/2

y = 25 1/2

We have 25 1/2 cows...

 

Substituting into our 2nd equation:

2x + 2(25 1/2) = 25

2x + 51 = 25

2x = 25-51

2x = -26

x = -13

 

We have -13 chickens.

 

Check the answers by plugging into our original equations.

 

2x + 4y = 76

2(-13) + 4(25 1/2) = 76

-26 + 102 = 76

76 = 76

 

2x + 2y = 25    assuming all have 2 eyes

2(-13) + 2(25 1/2) = 25

-26 + 51 = 25

25 = 25

 

The answers check.  With the information given you have

25 1/2 cows and -13 chickens.

Answer 2

Haleigh,

 

This is a nice word problem relating a system of equations using two variables: the number of cows and chickens. The first equation counts eyes and the second counts feet. However, since cows and chickens both have two eyes each it is impossible to have 25 eyes. Please check your problem again. I saw variants of this problem online where they count heads and feet, which is more likely.