Main content

## Modeling with linear inequalities

Current time:0:00Total duration:4:20

# Interpreting two-variable inequalities word problem

CCSS Math: HSA.CED.A.3

## 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.