Question 195257
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Can't be done.


Since the prices of cows and pigs are even numbers, the sum of the cost of all the cows and pigs purchased must be an even number as well.  Subtracting an even number from 100 results in an even whole number.  Therefore the only possible quantities of chickens that could be purchased must be even multiples of 8.  In other words you could buy 0, 16, 32, 48, 64, 80, or 96 chickens.


If you buy 0 chickens, you must spend the entire 100£ on 100 animals each of which has a price per each > 1£.  Impossible.


If you buy 16 chickens, you must spend 98£ on 84 animals.  You would use up the entire 98£ on 49 pigs, leaving you short 35 animals with no money left.


If you buy 32 chickens, you must spend 96£ on 68 animals.  Same problem, you use up your 96£ buying 48 pigs and you are 20 animals short of your goal.


If you buy 48 chickens, you must spend 94£ on 52 animals.  Again, your 94£ gets you at most 47 pigs -- still 5 animals too few.


If you buy 64 chickens, you have 92£ to spend on 36 animals.  Now we are getting into the realm of possibility, but:


Let <b><i>x</i></b> represent the number of cows and let <b><i>y</i></b> represent the number of pigs, leaving us with the following situation:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x + y = 36]  Number of animals


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 10x + 2y = 92]  Cost of animals


Solving this system of equations is left as an exercise for the student, but suffice it to say that, were this the appropriate solution, you would have to purchase fractional parts of cows and pigs.  Therefore, this is not feasible.


If you buy 80 chickens, you have 90£ to spend on 20 animals -- but:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x + y = 20]  Number of animals


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 10x + 2y = 90]  Cost of animals


Again, this results in a non-integer solution.  Not feasible.


Finally, if you purchased 96 chickens, then you would have 88£ to spend purchasing 4 animals.  The best you would be able to do is purchase 4 cows for 40£ leaving you with all 100 animals, but 48£ unspent.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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