100 yuan Buy 100 chickens One of the problem solving

Buy 100 different types of chickens with 100 bucks. One solution

Title: Rooster 5 Dollars A, hen 3 dollars A, chick 1 Yuan 3 only.  How can i buy 100 chickens with 100 bucks? This chicken is sold somewhere.

Solution: Set Buy Rooster I only, buy hen J only, chick naturally is 100-i-j only

5*i+3*j+ (1/3) (100-I-J) =100//here can get i<=20;j<=33;

Gets:*i+8*j=200

Q:   i* How did 14+j*8==200 come????

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PS: Later found this seems a bit complicated, put on a simple and easy to understand solution
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100 yuan Buy 100 chickens One of the problem solving