how many cows and how many chickens does the farmer have?  TOPIC_SOLVED

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how many cows and how many chickens does the farmer have?

Postby babyZ on Tue Mar 31, 2009 4:07 pm

farmer has a total of 21 cows and chickens.togteher the animals have a total of 54 legs.how many cows and how many chickens does the farmer have?

i got 15 chickens & 6 cows.how do u do the math 2 get the ans?
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Re: how many cows and how many chickens does the farmer have?

Postby little_dragon on Tue Mar 31, 2009 4:59 pm

every pair of chickens and cows has 6 legs. if you have 10 of each you have 10pairs wtih 60 legs, plu s whatever is left over. thats too much so start swapping. if you take out a cow and add a chick, you get tworid of 2 legs. if the extra is a cow, then 21 is 64 legs. you need 54 legs, so 5 swaps: take 5 cows out and put 5 chickisn in. this makes 5+1 cows (for the extra) and 15 chickens = 21 animals with 6*4+2*15=24+30=54 legs.

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Re: how many cows and how many chickens does the farmer have?  TOPIC_SOLVED

Postby Martingale on Tue Mar 31, 2009 7:32 pm

babyZ wrote:farmer has a total of 21 cows and chickens.togteher the animals have a total of 54 legs.how many cows and how many chickens does the farmer have?

i got 15 chickens & 6 cows.how do u do the math 2 get the ans?


let be the number of cows
let be the number of chickens

then

and the number of legs gives us the equation

solving the first equation for gives

now put this into the other equation



and solve for

then find

or you can set up an augmented matrix and row reduce is you know anything about matrices.
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