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and gauzy I think that's how I would pronounce it in Ghazi Ghazi needs to send out 300 wedding invitations in let me underline that 300 wedding invitations in one minute in one minute she can put six invitations in two envelopes and apply stamps to them it takes her a minimum of fifty seconds to address each invitation by hand if n represents the number of invitations and gauzy can prepare for mailing in 180 minutes in 180 minutes which of the following inequalities best models the situation described above so over here you have 180 greater than or equal to something it's in terms of N in terms of the number of invitations is 180 greater then this is 300 less than or equal to this is 300 less than right over here now remember what our constraint is here our constraint is how many can she prepare in 180 minutes how many invitations can she prepare in 180 minutes and so it feels like and I haven't done the math here that you're gonna want one of them that deals with 180 and since you can do it up to 180 that you would want not just not just the amount of time is less than 180 but it would have to be less than or equal to or 180 doesn't just need to be greater than the amount of time it could be greater than or equal to as long as this is equal to 180 we are fine so without doing any math I'm already feeling that this right over here is going to be the answer the 300 they're getting this from the fact that there's 300 that there's 300 wedding invitations that there's 300 wedding invitations to make now that is the absolute cap that is the absolute cap on the total of a number of wedding invitations that she that she might be able to do but that's not going to be that's that's not the constraint that we're talking about we're constraining her actual time here so let's verify that we feel good about this and it looks like they did everything in minutes so let's do everything in minutes so anyone any one envelope so let's see in one minute she can put six invitations into envelopes so anyone in tation I guess I could say how much will she spend tot how much time would she spend stick it into sticking it into an envelope and applying stamps what she's going to spend a sixth of a minute so she's going to spend one sixth of a minute I'm gonna do everything in minutes because these look like they're in minutes right over here a sixth of a minute putting anyone invitation into an envelope and putting stamps on them and then how much time will she spend writing the address well she's going to spend fifty seconds to write the address for any one invitation but if it's in terms of minutes that's fifty out of 60 seconds in a minute or so we could write this we could write this plus five six five six of plus five six of a minute and I'm really tempted to add these because they add up to one two six six but it doesn't look like they added them over here so I'm gonna keep him like this so this is how much time in minutes she would spend on anyone on any one invitation and then if she's doing n if she's doing n invitations well that's this is per invitation and then you multiply it by n so times and this is the total amount of time she would spend if she did end invitations and so this thing right over here has to be less than or equal to 180 so we could write it like this we could say less than or equal to 180 or we could say that 180 or we could write that 180 is going to be greater than or equal to that and if you distribute the N if you distribute the end you're gonna get this thing right over here you're going to get 180 is greater than or equal to and over six and over six plus plus 5n actually let me write it that way plus 5 times and 5 times n / 6 / / that blue color over 6 which is exactly what you have here but it's really interesting because just looking at the choices actually jumped out pretty fast that this was probably going to be the one that we cared about