Farmer Charlie has a chicken farm. On a certain day, Charlie calculates in how many days he will run out of chicken-food. He notices that if he would sell 75 of his chickens, he could feed the remaining chickens twenty days longer with the chicken-food he has, and that if he would buy 100 extra chickens, he would run out of chicken-food fifteen days earlier.
How many chickens does farmer Charlie have? Choose the correct answer:
A) 100 B) 500 C) 300 D) 400 E) 600
C   300   Let n be the number of chickens and let d be the number of days in which Charlie will run out of chicken-food with this number of chickens. The total amount of chicken-food always equals the number of chickens multiplied by the number of days the food lasts. Therefore, the total amount of chicken-food equals n × d.   If Charlie would sell 75 of his chickens, he could feed the remaining chickens twenty days longer, so the total amount of chicken-food would then equal   ( n - 75 ) × ( d + 20 ).   But the total amount of chicken-food does not change, so   ( n - 75 ) × ( d + 20 ) = n × d   which can be rewritten to equation 1:   d = 4/15 × n - 20.   If Charlie would buy 100 extra chickens, he would run out of chicken-food fifteen days earlier, so the total amount of chicken-food would then equal   ( n + 100 ) × ( d - 15 ).   But the total amount of chicken-food does not change, so   ( n + 100 ) × ( d - 15 ) = n × d   which can be rewritten to equation 2:   d = 3/20 × n + 15.   Combining equations 1 and 2 gives:   4/15 × n - 20 = 3/20 × n + 15.   Solving this equations gives n = 300, so farmer 300harlie has 300 chickens.
<result>C</result>
Farmer Charlie has a chicken farm. On a certain day, Charlie calculates in how many days he will run out of chicken-food. He notices that if he would sell 75 of his chickens, he could feed the remaining chickens twenty days longer with the chicken-food he has, and that if he would buy 100 extra chickens, he would run out of chicken-food fifteen days earlier.
How many chickens does farmer Charlie have?