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## SAT (Fall 2023)

### Course: SAT (Fall 2023) > Unit 10

Lesson 1: Heart of algebra- Solving linear equations and linear inequalities — Basic example
- Solving linear equations and linear inequalities — Harder example
- Interpreting linear functions — Basic example
- Interpreting linear functions — Harder example
- Linear equation word problems — Basic example
- Linear equation word problems — Harder example
- Linear inequality word problems — Basic example
- Linear inequality word problems — Harder example
- Graphing linear equations — Basic example
- Graphing linear equations — Harder example
- Linear function word problems — Basic example
- Linear function word problems — Harder example
- Systems of linear inequalities word problems — Basic example
- Systems of linear inequalities word problems — Harder example
- Solving systems of linear equations — Basic example
- Solving systems of linear equations — Harder example
- Systems of linear equations word problems — Basic example
- Systems of linear equations word problems — Harder example

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# Linear inequality word problems — Harder example

Watch Sal work through a harder Linear inequality word problem.

## Want to join the conversation?

- Instead of it being "n/6 + 5n/6", shouldn't it have been "n/6 + 0.5n/6"? I am asking this because if the "n" is equal to 1 minute in the equation, and "5n" is equal to 50 seconds, then the 50 seconds should be represented as "0.5n". If I am wrong may someone please explain this to me?(32 votes)
- .5 would equal half of a minute which would be 30 seconds. 5/6 works because it is 50 out of 60 seconds.=50/60 which equals 5/6. Then you distribute the n.(10 votes)

- How do you get 1/6? I'm a little bit confused about it.(21 votes)
- You can make a proportion to represent the amount of time it takes Ngozi to put 1 invitation in an envelope and apply stamps to them. In the problem, it's given that it takes Ngozi 1 minute to put 6 invitations in envelopes and apply stamps to them. So, if it takes her 1 minute to deal with 6 invitations, how many minutes will it take her to deal with 1 invitation? You can set up the proportion (1 minute / 6 envelopes) = (x minutes / 1 envelope). Cross multiply and solve for x, and you get x=1/6! So it takes Ngozi 1/6 of a minute to put 1 invitation into an envelope and apply stamps to.(41 votes)

- I still don't get why he chose the answer with the greater or equals sign if the question was asking how many Ngozi could make within 180 minutes, so it shouldn't extend that time, right?(23 votes)
- It's because Ngozi might be able to complete all 300 in less than 180 minutes, but Ngozi has up until 180 minutes to finish them. If Ngozi manages to complete all 300 before the 180 minutes has elapsed, then she does not need to use the rest of her time, but if she doesn't finish early, then the equation will show how many she will complete in exactly 180 minutes. Therefore, it shows how many she completes in less than or equal to 180 minutes.(10 votes)

- I'm confused on how the 50 seconds could be represented in 5/6? Isn't the 6 the amount she makes in one minute? How does that connect with the 50 seconds?(10 votes)
- Ngozi spends 50 seconds addressing each invitation by hand. Since she can stamp 6 envelopes in 1 minute, that would be the proportion 1 minute per 6 envelopes, or 1/6. Then, she spends 50 seconds addressing each envelope. Since we are talking in terms of minutes, and 1 minute equals 60 seconds, that would be 50 seconds of addressing for every 60 seconds, or 50/60, which, after cancelling, reduces to 5/6. Then you multiply the two ratios, 1/6 and 5/6, by n: n((1/6) + (5/6)) -> (n/6) + (5n/6). And since we are talking about how many invitations Ngozi can complete in 180 minutes, the final inequality looks like: 180 ⪈ (n/6) + (5n/6).

Hope that helps! 😉(10 votes)

- So basically 180 is greater than or equal to n(13 votes)
- At3:26(roughly), how can he say that the inequation would be less than or equal to 180? I'm a little confused.(11 votes)
- how to use a graphic calculator pleasemake a tutorial(7 votes)
- do you have bacon and ham o great and mighty khan ruler of Mongolia(5 votes)
- The Question says,"It take her a min of 50 sec to address invitation by hand." Doesn't this expression need some expression because the time maybe 50 sec or more. Can we simply express it like 5n/6 ? Look my question is 5n/6 just mean it take 5/6 min per invitation but the fact is not like that. it may greater than 5/6. So I think there is a gap in the question or in the answers, in my opinion.(4 votes)
- At2:33, How did you get 5/6? when Ngozi takes a minimum of 50 seconds to hand address the invitations.(4 votes)

## 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.