Justin has 20 pencils, 25 erasers, and 40 paper clips. He organizes the items in each into groups with the same number of group. All the items in a group will be the same type. How many items can he put in each group?

May 27, 2017

Justin can put 4 pencils, 5 erasers, and 8 paperclips into 5 different bags.

Explanation:

Justin wants to divide up pencils, erasers and paper clips into equal quantities. Presumably, if he hands these out to people, the recipients will have the same amount of some pencils, some erasers, and some paper clips.

The first thing to do is find a number that evenly divides into all three. That is, a number that divides evenly into 20, 25, and 40. It seems clear that the number 5 will do the job. This is because

Pencils: $20 \div 5 = 4$
Erasers: $25 \div 5 = 5$
Paper clips: $40 \div 5 = 8$

The answer flows freely from this realization. Justin can put 4 pencils, 5 erasers, and 8 paperclips into 5 different bags. If he hands out the bags, 5 different recipients will have the same things in each bag.