How many chickens did the farmer have at first?

Question

A farmer had twice as many chickens as ducks on his farm.  After he sold 166 chickens and 29 ducks, he had half as many chickens as ducks left.  

Answer 1

Hi Karen;

 

First, what are we looking for?  How many chickens did he start with?

Assign variables for the unknowns:

 

Let c = # chickens

Let d = # ducks

 

Now, from the information given make equations:

 

farmer had twice as many chickens as ducks :

c = 2d   {equation 1}

 

After he sold 166 chickens and 29 ducks, he had half

as many chickens as ducks left:

c - 166 = (d-29)/2  {equation 2}

 

Since c=2d, substitute that into equation 2:

 

2d - 166 = (d-29)/2

 

multiply through by 2

 

4d - 332 = d - 29

 

on each side subtract d and add 332

 

3d = 303

 

d = 101 ducks

c = 2d = 202 chickens

 

Check:  202 - 166 = (101-29)/2

              36 = 36

This checks as correct.