Final answer:
The inequality representing the number of matching invitations Alan can buy without exceeding his limit of 100 is 2x + y ≤ 100, where x is the number of invitations per box and y is the number of extra personalized invitations.
Step-by-step explanation:
The question is asking how to represent the number of matching invitations Alan can buy while remaining within his limit of 100 total invitations using inequalities. If Alan is buying 2 boxes of matching invitations and some extra personalized invitations, we need to determine the total quantity of invitations he can purchase in each box to not exceed 100 when doubled.
Let x represent the number of matching invitations in each box. Since Alan is also buying an unspecified number of extra personalized invitations, let's assume the number of extra invitations is y. The inequality will be formed by understanding that twice the number of invitations in one box plus the extra invitations should be less than or equal to 100, which is his limit.
The inequality will therefore be: 2x + y ≤ 100
This represents the maximum number of invitations Alan can send without going over his limit. Since we don't have the specific number of extra personalized invitations, only the variable y is included in the inequality for those.