Ben Has Only Ducks And Cows. He Knows He Has 22 Animals In All. He Knows The Total Amount Of Legs Are 56. How Many Of Each Animal Does He Have?

4 Answers

Farah Faith Profile
Farah Faith answered
The problem can be solved in the following way:
 
Say, the number of cows Ben have is x and the number of ducks Ben have is y
 
Therefore, total number of cows and ducks is x+y=22 ------ (I)
 
If one cow has 4 legs, then x cows will have 4x legs
Also, if one duck has 2 legs, then y ducks will have 2y legs
 
Therefore, total number of legs is 4x+2y=56 ------(ii)
 
Equations (I) and (ii) will be solved now
From (I), x=22-y
 
Putting the value of x from (I) in (ii),
4(22-y)+2y=56
88-4y+2y=56
-2y=-32
y=16
 
Putting the value of y in equation (I)
x=22-16
x=6
 
Therefore, the number of cows is 6 and the number of ducks is 16
Anonymous Profile
Anonymous answered
Draw 22 animals that are all ducks (2 legs). The animals can just be circles with two lines coming out as legs. You will have 44 legs. Then begin creating cows out of ducks one at a time until you get to the correct number of cows (should be 6 cows and 16 ducks). This is an exercise in problem solving and when math teachers give it out they mean for you to try new things (like draw a picture)
Anonymous Profile
Anonymous answered
There are a couple  of options.... Since cows have 4 legs and ducks 2.

4 legs = 1 cow

2 legs= 1 duck 

start with the cows and do multiples of 4, and then divide the result by two

4 x 5 (cows) = 20 (legs)
56 (total legs) - 20 =36
36/2= 18

so if you have 5 cows, you'll have 18 ducks

-- another possiblity
for 10 cows:
4x 10= 40 legs
56- 40= 16
16 divided by 2 = 8 ducks

so if you have 10 cows, you can have 8 ducks
thanked the writer.
Farah Faith
Farah Faith commented
Your solution is wrong. You can check it by adding the total number of cows and ducks u have found. In one solution u got... 5 cows and 18 ducks, so the total makes 23. The other solution says 10 cows and 8 ducks, which makes a total of 18. Both of these are wrong, since the question clearly says that the total number of animals is 22.

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