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

Fractions, ratios, percentages, exponents, number patterns, word problems without variables, etc.

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

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?
babyZ

Posts: 24
Joined: Thu Mar 12, 2009 5:27 pm

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

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.

little_dragon

Posts: 188
Joined: Mon Dec 08, 2008 5:18 pm

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

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 $x$ be the number of cows
let $y$ be the number of chickens

then $x+y=21$

and the number of legs gives us the equation $4x+2y=54$

solving the first equation for $x$ gives $x=21-y$

now put this into the other equation

$4x+2y=54\Leftrightarrow 4(21-y)+2y=54$

and solve for $y$

then find $x$

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

Martingale

Posts: 363
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA