Required a mathematical solution of the problem

Hello Friend .............

Here is a problem stated as:

Let there is a milkman who requires 40 liter of milk a day. constraint is that he can have exactly 19 animals. and the animals he can choose are as below with their capability of giving milk.

Cow can give 2 liters a day.
Buffalo can give 5 liters a day. and
Goat can give (1/4) liter a day.

This problem's solution is:
No of Cows =12 milk produced = 12 * 2 = 24
No of Buffaloes = 3 milk produced = 5*3 = 15
No of Goats = 4 milk produced =(1/4) * 4 = 1
No of animals =19 milk produced =40 liters

Now Problem is that is there any system of liner equations that can be used to get answer of such type of problems, Trial and error methods is not needed.


Thank you all........

Quote:

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Originally Posted by shailesh1987

Hello Friend .............

Here is a problem stated as:

Let there is a milkman who requires 40 liter of milk a day. constraint is that he can have exactly 19 animals. and the animals he can choose are as below with their capability of giving milk.

Cow can give 2 liters a day.
Buffalo can give 5 liters a day. and
Goat can give (1/4) liter a day.

This problem's solution is:
No of Cows =12 milk produced = 12 * 2 = 24
No of Buffaloes = 3 milk produced = 5*3 = 15
No of Goats = 4 milk produced =(1/4) * 4 = 1
No of animals =19 milk produced =40 liters

Now Problem is that is there any system of liner equations that can be used to get answer of such type of problems, Trial and error methods is not needed.


Thank you all........

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(Hi)

As far as I can think I don't see any method devoid of trial and error "completely", hope to see it(Giggle)

Lets take "m" buffaloes , n cows and 4k(Why!!----total milk produced is 19 , an integer) goats

where "m" "n" and "k" are integers





Try bringing last equation in terms of "k" and any one of "m" and "n"

This is what I got



Now since m<8(Why!! ---milk=40) , its better if you try to put the values till the first time you get an integer ...that's your answer

A slight typo
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Lets take "m" buffaloes , n cows and 4k(Why!!----total milk produced is 40 , an integer) goats................