Question 305751
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Let *[tex \Large g] represent the number of goats.


Let *[tex \Large c] represent the number of chickens.


Presuming that we have no 2-headed chickens or 3-legged goats, which is to say that we presume all goats have one head and four feet while all chickens have one head and two feet, we can make the following assertions:


1:  *[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4g\ +\ 2c\ =\ 150]


2:  *[tex \LARGE \ \ \ \ \ \ \ \ \ \ g\ +\ c\ =\ 70]


Multiply the second equation by -2:


3:  *[tex \LARGE \ \ \ \ \ \ \ \ \ \ -2g\ -\ 2c\ =\ -140]


Add equation 1 to equation 2:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2g\ +\ 0c\ =\ 10]


So


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ g\ =\ 5]



Five goats means 65 chickens.


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