Carol was sending out birthday invitations to w friends. If each package of invitations she bought had x invitations in it How many packs does she need so that no friend gets left out?
Carol has w friends. 
Each package of invitations has x invitations in it. 
Carol needs to buy p packages of invitations. 

We need to find p. 

We know that w = p * x. 

We also know that p must be an integer, which means that w must be a multiple of x. 

Therefore, we need to find the smallest integer p such that w is a multiple of x. 

The smallest integer p such that w is a multiple of x is w / x. 

Therefore, the number of packages of invitations Carol needs to buy is w / x.