Main content

## Integrated math 1

### Course: Integrated math 1 > Unit 7

Lesson 3: Modeling with linear inequalities- Writing two-variable inequalities word problem
- Solving two-variable inequalities word problem
- Graphs of two-variable inequalities word problem
- Two-variable inequalities word problems
- Interpreting two-variable inequalities word problem
- Modeling with systems of inequalities
- Writing systems of inequalities word problem
- Solving systems of inequalities word problem
- Graphs of systems of inequalities word problem
- Systems of inequalities word problems
- Analyzing structure with linear inequalities: fruits
- Analyzing structure with linear inequalities: balls
- Analyzing structure with linear inequalities

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Interpreting two-variable inequalities word problem

Sal analyzes a two-variable linear inequality that models a context about YouTube videos.

## Want to join the conversation?

- It's over 9000

Well over 9000 comments(30 votes) - "over nine thousand!"(19 votes)
- Well that’s what he wants. Over 9000(6 votes)

- It's over 9000!(16 votes)
- I wounder if he knew what he was doing with these anime references(13 votes)
- how do you know that 750 is the number of comments and not the number of videos?!(5 votes)
- It says

"In the following inequality, C represents the number of cat videos..."

It's telling you that the variable C represents how many cat videos there are. The coefficient 750 represents how many comments each cat video has.

If there are C number of cat videos and there are 750 comments on each cat video, then the total number of comments from all the cat videos is going to be 750 comments per cat video times the number of cat videos (C). So it's going to be 750C.(8 votes)

- I actually got this exact question in the problems. Shouldn't khan academy make it so that that doesn't happen, for obvious reasons?(5 votes)
- the same thing has hapend to me befor(4 votes)

- why not a cat and dog video(a cat and a dog in the same video)?(1 vote)
- I got this question before I watched this. Did this happen to anyone else?(6 votes)
- How did Sal get 750 and 450 for each variable?(2 votes)
- Steven,

Those constants are given. It would be better if the word problem stated it outright.(2 votes)

- Its over 9000!!(2 votes)

## Video transcript

- [Voiceover] "Goku wants
to get over 9000 comments "on his YouTube videos. "He gets to the same number of comments "for each cat video that he uploads, "and he gets the same number of comments "for each dog video that he uploads." That's somewhat amazing. The exact same number of
comments for each cat video and the exact same number
for each dog video. But we'll just assume
what they're telling us. "In the following inequality, C represents "the number of cat videos, C for cat, "and D represents the
number of dog videos, "D for dog, dog videos
that Goku should upload "to achieve his goal." So 750 times the number of cat videos plus 450 times the number of dog videos needs to be greater than 9000. "According to the inequality, "how many comments does each cat video get "and how many comments
does each dog video get?" So let's see if we understand
what's going over here, what's going on in this inequality
to answer their question. So he wants to get over 9000 comments and we see that right over here. He wants to get over 9000 comments. So this we could view as a number of comments that he actually gets. Since we have some number times C, we can assume that, well C, well we know that C is
a number of cat videos and so the number times C, that's the number of comments that he gets from cat videos. And on a per cat video bases, he's going to get 750 comments. Because if I say, "Hey, look. "I have C cat videos and on each of them, "I have exactly 750 comments." Well, I'm gonna have 750 times C comments on all of my cat videos combined. So each cat video gets 750 comments. And similarly, I can never say that, each dog video gets, well this is the total number
of comments from dog videos. You add all of these together. Your total number of comments w to be greater than 9000. Well, if the total from
dog videos is 450 D, then we see he's getting
450 comments per dog video. 450 comments per video times
the number of dog videos gets the total comments from dog videos. So he gets 450 comments per dog video. "Can Goku achieve this goal
by uploading eight cat videos "and seven dog videos?" So let's think about this. Eight cat videos, seven dog videos. So let's see. If we have 750, let me
do those in same colors, if we have 750 times eight, times eight plus 450 times seven, is this greater than, I'm writing the question
mark so we don't know, is this going to be greater than 9000? Well, we just have to evaluate this. What is this going to be? Let's see. 700 times eight is 5600. It's going to be 5600 plus another 50 times eight is 400. So 5600 plus 400 is 60 hundred or 6000. So this is 6000 right over here. So that would be, if he
has eight cat videos, he gets 750 comments per video so he's going to have a
total of 6000 comments on all of the eight cat videos combined. And then 450 times seven, let's see, 400 times seven is 2800 plus another 30, plus another 350, that's going to be, what? 3150, is that right? Let's see, that would be, let me show you to this right, 2800 plus 400 times seven is 2800. 50 times seven is 350. Yep, I think that is right. It all, all works out, 3150. So 6000 plus 3150 is
indeed greater than 9000. It is indeed greater than 9000. This over here is 9150 which is indeed greater than 9000. So yes, he can achieve his goal by uploading eight cat
videos and seven dog videos.