If the farmer sells 75 of his chickens, his stock of feed will last for 20 more days than planned, but if he buys 100 more chickens, he will run out of feed 15 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. How many chickens does the farmer have?
Choose the correct choice from the following.
A) 60
B) 120
C) 240
D) 275
E) 300

Rationale: let v denote the volume of feed one chicken consumes per day . then the total volume of feed in stock will be v ∗ d ∗ c where d is the number of days the feed will last if the number of chickens does not change and cc is the current number of chickens . from the question it follows that v ( d + 20 ) ( c − 75 ) = vdc v ( d − 15 ) ( c + 100 ) = vdc the first equation simplifies to 20 c − 75 d = 1500 . the second equation simplifies to ( − 15 ) c + 100 d = 1500 after dividing everything by 5 we get the linear system : 4 c − 15 d = 300 ( − 3 ) c + 20 d = 300 solving it we get c = 300 d = 60 answer : e
Answer: E