C. 970. Rose, Ivy and Violet decided to solve all problems in their book of mathematics problems. Rose solves a problems, Ivy solves b problems and Violet solves c problems a day. (Each problem is only solved by one of the girls.) If Rose solved 11 times as many problems a day, Ivy solved 7 times as many and Violet solved 9 times as many, they would finish the job in 5 days. If Rose solved 4 times as many, Ivy solved 2 times as many and Violet solved 3 times as many problems a day, they would take 16 days. How many days does it take them to get done with the solutions?
Deadline expired on 16 February 2009.
Google Translation (Sorry, the solution is published in Hungarian only.)
Megoldás. Felírhatjuk a következő egyenletet:
amiből rendezés után kapjuk, hogy:
Ez valóban lehetséges, ha pl. a=c=1 és b=4, és a feladatok száma 240.