Bunuel wrote:

Official Solution:

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?

A. 60

B. 120

C. 240

D. 275

E. 300

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 \(C\) 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 \(20C - 75D = 1500\). The second equation simplifies to \((-15)C + 100D = 1500\). After dividing everything by 5 we get the linear system:

~~\(4C - 15D = 300\)~~

\((-3)C + 20D = 300\)

Solving it we get \(C = 300\), \(D = 60\).

Answer: E

Hi Bunuel,

Initially I tried to solve with direct proportion formula (Rate x Number = Total Days), but finally equations results in this: (D + 20)/(C - 75) = (D - 15)/(C + 100) . Why does this formula does not work? Is it because is for direct proportionality and in this case the problem is for INdirect proportionality? I am confused, could you help me?

Thanks a lot.

Best regards.

Luis Navarro

Looking for 700