1. Name:______________________________ Date:________________
Reason the Numbers
Directions Complete all of the following problems. Make sure to show all of your work and explain!
1. Jake is planning a cookout. He knows that hot dogs come in packages of 10 and hot dog rolls come in packages of 8. If Jack wants an equal number of hot dogs and rolls, what is the minimum number of packages of each that he must purchase?
What other combinations of packages could he purchase to have an equal number of hot dogs and rolls?
2. Three pieces of timber 42 m, 49 m and 63 m long have to be divided into planks of the same length. What is the greatest possible length of each plank ?
3. Say you have 60 pencils, 90 pens and 120 tablets and you want to make packages of pencils, pens and tablets to donate to your school for students who cannot afford these supplies. What is the maximum number of packages you can make using all items, and how many pencils, pens and tablets will be in each package?

2. 4. One trip around a running track is 440 yards
4. One trip around a running track is 440 yards. One jogger can complete one lap in 8 minutes, the other can complete it in 6 minutes. How long will it take for both joggers to arrive at their starting point together if they start at the same time and maintain their jogging pace?
5. There are 100 lockers in the school hallway. Kim will put a sticker on every 4th locker and Juan will put a balloon on every 6th. How many lockers will have stickers? How many lockers will have balloons? How many lockers will have both?
6. A bag of marbles can be shared equally among 6, 12 or 15 students with none left over. What's the least amount of marbles that can be in the bag?
7. I am thinking of 2 numbers, 12 and another number. 12 and my other number have a greatest common factor of 6 and their least common multiple is 36. What's the other number I'm thinking of?
8. The greatest common factor of two numbers is 30. Their least common multiple is 420. One of the numbers is 210. Can you find the other number?