Question

Marcus bought a two-pound bag of Skittles with 900 pieces of candy in it. He wants to share whole pieces of candy fairly with one of his groups of friends. He does not want to cut the candies into pieces. Marcus could split the candy 11 ways by sharing with his soccer teammates. Marcus could split the candy 18 ways by sharing with his school friends. With whom should he share his candy so that the pieces are evenly distributed (nothing is leftover)? Explain your thinking.

a) Marcus should share with his soccer teammates.
b) Marcus should share with his school friends.
c) Marcus should share with both groups to ensure fairness.
d) Marcus should eat the candy himself because it cannot be evenly split.

Answer 1

Marcus should share with his school friends because 198 is a divisor of the 900 pieces of candy.

Step-by-step explanation:

In order for Marcus to share the candy evenly, he needs to find a number that can be divided by both 11 and 18 without any remainder. This number is called the least common multiple (LCM) of 11 and 18. To find the LCM, we can list the multiples of both 11 and 18 and find the smallest number that appears in both lists.

The multiples of 11 are: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110...

The multiples of 18 are: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180...

The LCM of 11 and 18 is 198. Since the bag of candy has 900 pieces, Marcus should share it with his school friends, as 198 is a divisor of 900. This means that each person in his school group can get their fair share of 900 pieces of candy.