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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? • How do you get 1/6? I'm a little bit confused about it. •  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.
• 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? • 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.
• 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? • 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! 😉
• So basically 180 is greater than or equal to n • At (roughly), how can he say that the inequation would be less than or equal to 180? I'm a little confused. • how to use a graphic calculator pleasemake a tutorial • 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.   