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

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. 
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.
Respond to this Question
Similar Questions

math
A farm has cows and ducks. There are 78 feet and 27 hands. How many of each animal are there? 
Math
How many line segments can be drawn between each 15 points? 
Maths
A farm rears 9 ducks and cows in his farm. There are 28 legs altogether.How many ducks are there in the farm? 
maths
the total number of cows and ducks on a farm is 35.All the cows have 74 more legs than all the ducks.How many cows are there on the farm? 
maths
the total number of cows and ducks on a farm is 35.All the cows have 74 more legs than all the ducks.How many cows are there on the farm? 
Math
Old McDonald has cows and chickens on his farm. If the animals on his farm have a total of 197 heads and 634 legs, how many cows does Old McDonald have? 
maths
There are a total of 50 ducks and goats in a farm. They have 154 legs altogether. How many ducks are there? 
Math
Mohammed had ducks and cows on his farm. These 14 animals had a total of 40 legs. How many each animals did Mohamed have? 
Math
Mr McDonald has some ducks and goats in his farm. If he counted a total of 94 legs and 30 heads, find the number of ducks and the number of goats in his farm. 
Math
There are 42 goats and chickens in the farm.there are 114 legs altogether.how many ducks are there?