Answer to Question #85865 in Algebra for Archana Kolli

Question

A bag contains red and green marbles. For every 5 marbles Jackie picks, at least 1 marble is red. For every 6 marbles Jackie picks, at least 1 marble is green. What is the largest number of marbles that the bag can contain?

Answer 1

Rephrasing the described situation: among every 5 marbles at least 1 marble is red, this is the same as to say that at most 4 marbles are green. Hence, there are at most 4 green marbles in the bag. (Otherwise, if a bag contained more than 4 green marbles, Jackie could pick 5 marbles none of which is red because all of them are green.) Similarly, among every 6 marbles at least 1 marble is green, this is the same as to say that at most 5 marbles are red. Hence, there are at most 5 red marbles in the bag. (Otherwise, if a bag contained more than 5 red marbles, Jackie could pick 6 marbles none of which is green because all of them are red.)

Altogether the bag can contain at most 4 green and 5 red marbles, totally 4+5=9 marbles.

Answer:

9 is the largest number of marbles that the bag can contain.