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### Course: 7th grade (Illustrative Mathematics) > Unit 2

Lesson 5: Lesson 6: Using equations to solve problems# Writing proportional equations

Sal figures out the constant of proportionality when dealing with a constant rate.

## Want to join the conversation?

- who else doesnt pause the video(16 votes)
- I never pause thee vid so upvote if you never pause vid 😁👍🏻(46 votes)

- I am still confused(30 votes)
- All you have to do is divide the numbers given and put the number you get in between two variables! ex d=8.5h(4 votes)

- "Scarlett is playing a video game. She spends 900 minerals to create 18 workers. Each worker costs the same number of minerals.

Write an equation to describe the relationship between m, the amount of minerals, and w, the number of workers."

For this Question, my equation was: m=50w, and it marked me wrong. Isn't it supposed to be correct because for each worker she uses 50 minerals.

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My work: I started off with 900/18 to find the unit rate, (50) and found out that that was the number of minerals used to make 1 worker. You need to multiply 50 by the number of workers to find out the total amount of minerals you used up. I am right, right?(23 votes)- Hmmm... that does seem correct... Did you check what they had the answer as? Perhaps they wanted it to be w=?m, since that would tell how many minerals per worker, and how much of the minerals goes toward each worker. I am not sure, but it is always a good idea to check through Khan Academy's work, so you can see what could've gone wrong!! I bet this didn't really help very much, sorry!(9 votes)

- I've watched this thing like 3 times and it still says I didn't do it.(9 votes)
- Lol try closing and restarting the page

upvote if it helped(27 votes)

- How can you use rates and proportional relationships in the real world?(16 votes)
- A unicorn daycare center requires there to be 2 supervisors for every 18 baby unicorns.

Write an equation that shows the relationship between nnnn, the number of supervisors, and uuuu, the number of baby unicorns.

Please note that this is a magical daycare center, so fractional supervisors are allowed.

do they cut a supervisor in half and take it with them?(8 votes) - i watched this 5 times and it says it is unfinished!!1111(5 votes)
- You have to watch through the entire thing without skipping any parts.(5 votes)

- How is it D=kh? Isn't it susposed to be K= Y/X? because that's what were doing in school.(5 votes)
- D=kh: Distance=Constant Speed*Time

In your equation, K=Constant Speed, Y=Distance, X=Time

I learn D=Vt (Distance=Velocity*Time)(4 votes)

- why is it so difficult(6 votes)
- I DONT GET THISS literally anything ;’((4 votes)

## Video transcript

- [Instructor] We're told that Justin runs at a constant rate, traveling
17 kilometers in two hours. Write an equation that
shows the relationship between the distance he
runs, d, in kilometers and the time he spends
running, h, in hours. So, pause this video and see
if you can work through that on your own before we do it together. All right, now there's several ways to approach this question. One way is to say, look, he's
running at a constant rate, so his distance is going to
be equal to some constant, let's just call that lowercase k, times the amount of
time he spends running, and the way that we can
figure out what k is is by using the information
that they gave us. They tell us right over here that when our distance is 17 kilometers, so when our distance is 17 kilometers, that's a situation where he
has been running for two hours. So, that is going to be
equal to k times two hours. So, what is k going to be? Pause the video again and
see if you can figure it out, if you didn't figure it out the first time I asked you to pause the video. All right, well there's a
bunch of ways to solve for k, but one way is to say, let's just divide both sides by two hours. So, if you divide both sides by two hours, you are going to get that k is going to be equal 17 over
two kilometers per hour, which is, 17 over two is 8.5, 8.5 kilometers per hour. And so, if we go back to
the original question, which asks us to write an equation that shows the relationship
between d and h, we can say that d is equal to, we now know our proportionality constant, it is 8.5 times h. 8.5 times h, and we're done. If we wanted to write their units, we could write d is equal to 8.5 kilometers per hour times h, which is given in hours.