# Maths

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A farm rears 9 ducks and cows in his farm. There are 28 legs altogether.How many ducks are there in the farm?

• Maths -

d + c = 9
2d + 4c = 28

Multiply the top equation by -2 and add. This will give you the number of cows. Find the ducks by substituting into the first equation.

• Maths -

let d=number of ducks reared
c=number of cows reared
sum of ducks and cows=d+c=9
sum of their legs=2d+4c=28 since duck has two legs and cow also has 4 legs
the two equations give
d+c=9...1
2d+4c=28...2
multiply eqn 1 by 2
2(d+c=9) which gives 4d+4c=18..3
now 2d+4c=28
-2d+2c=18
we have 2c=10
therefore c=5 put c into eqn..1
to get d+5=9
d=4 meaning there are 4 ducks and 5 cows.proof2*4=8legs in all does 4 ducks and 4*5=20 legs in all does 5 cows.

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