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## Heart of algebra

# Linear inequality word problems — Harder example

## Video transcript

- [Narrator] Ngozi, I think
that's how it pronounced Ngozi gozi needs to send
out 300 wedding invitations. In, let me underline that. 300 wedding invitations. In one minute, she can put
6 invitations into envelops and apply stamps to them. It takes her a minimum of 50 seconds to address each invitation by hand. If n represents the number of invitations Ngozi can prepare for mailing 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. Its in terms of n. In terms of the number of invitations. Here is 180 greater than. 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 have done the math here that you are want one of
them that deals with the 180. And since you can do it up to a 180 that you would want not
just the amount of time that is less than 180, but it has to be less than or equal to or 180. Doesn't 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 am already feeling
that this right over here is going to be the answer. The 300 they are getting
this from the fact that there is 300 wedding invitations to make. Now, there is the absolute cap on the total of number
of wedding invitations that she might be able to do. But, that's not going to be that's not the constraint
that we are talking about. We are constraining her actual time here. So, lets verify that we
feel good about this. And it looks like they
did everything in minutes. So, lets do everything in minutes. So, any one envelope so, lets see in one minute she can put 6 invitations into envelopes. So, any one invitation,
I guess I could say how much was she spent how much time would she spent sticking into an envelope
and applying stamps? Was she going to spend
sixth of the minute? So, she is gonna spend
one sixth of a minute I am gonna do everything in am minute because its look like
there in minute over here. A sixth of a minute putting any one invitation
into an envelope and putting stamps on them. And than how much time would she spend on writing the address? Would she is gonna spend 50 seconds to write the address
for any one invitation? But, its in terms of minute that's 50 out of 60 seconds in a minute or so we could right this 5/6 of a minute. And I am really tempted to add these because they add up to 1 to 6, 6. But, it doesn't look like
they added them over here so, I am gonna keep them like this. So, this is how much time in minutes she would spend on any one invitation. And then if she is doing n invitations, well this is per invitation and then you multiply it by n so, times n, this is
a total amount of time she would spend if she did n invitations. Ans so, this thing right over here has to be less than or equal to 180. So, we could write it like this we 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 you are gonna get this
thing right over here. You are going to get 180
is greater than or equal to (n/6 + 5n/6). Which is exactly what you have here. But, it is really interesting because just looking at the choices actually jumped out pretty fast that this would probably
going to be the one that we cared about.