Word problem

Question

A poultry farm only has chicken and pigs. When the manager of the poultry counted the heads of the stock in the farm, the number totaled to 295. However, when the number of legs was counted, the number totaled up to 874. How many chickens were in the farm?

 

The answer is 153, I would like to know how. Thank you! :)

Answer 1

Hey!   Thanks for “wanting to know!”

The most important part of a word (story) problem is translating the words into math expressions;  after that, the math is easy.

We assume that each chicken and each pig has 1 head  (I will verify this because a often fed chickens and pigs as a kid on our farm).

And, each chicken has 2 legs and each pig has 4 legs (live chickens and pigs, of course)

The problem gives the total number of legs  (874) and asks for the number of chickens.
                The number of chicken legs + the number of pig legs  = 874

     Or                                      2*numberofchickens  + 4 *numberofpigs = 874
  And for heads                        numberofchickens  + numberofpigs   = 295

Let’s shorten this, for math, by assigning variables C and P:
          2C +4P  = 874
           C + P = 295

Now, you may either solve for P or C and substitute that value into the other equation or you may create a common coefficient of one of the variables and eliminate it by adding or subtracting equations.   I like elimination, so let’s multiply the second equation and subtract equations:

                2C   +   4P   =  874
                2C   +   2P   =  590         (second equation multiplied by 2)
             -----------------------------      (subtract the two equations)
                0      +   2P   =  284
                              P    =  142          (that’s a herd of pigs!)

Putting the number of pigs into the second equation:
                        C + 162 = 295
                        C  = 153

Checking (very important):
      Is 2*(153) + 4*(142)   = 874   ?
             306  +  568  = 874    Yes