Question

A store clerk is bagging spices. He has 18 teaspoons of cinnamon and 30 teaspoons of nutmeg. Each bag needs to contain the same number of teaspoons, and each bag can contain only one spice. How many teaspoons of spice should the clerk put in each bag? How many bags of spice will there be?

1. RobertKer
By finding the maximum common factor between the number of spoons, we conclude that he must put 6 teaspoons per bag.
There will be 8 bags in total.

### How many teaspoons of spice should the clerk put in each bag?

We know that the store clerk has 18 teaspoons of cinnamon and 30 spoons of nutmeg.
Now, we want to put these in bags, such that each bag contains the same number of teaspoons.
Then the number of teaspoons per bag must be a common factor of 30 and 18. (the minimum number of bags is what we get when we select the maximum common factor).
Decomposing these two numbers gives:
30 = 2*3*5
18 = 2*3*3
Then the maximum common factor is 2*3 = 6
This means that we need to put 6 teaspoons per bag.
And the total number of teaspoons is 30 + 18 = 48, dividing that by 6 we get:
48/6 = 8
There will be 8 bags.