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Linear equations word problem: marbles

Sal finds the y-intercept and the slope of a linear relationship representing someone filling a glass tank with marbles. He then interprets what the y-intercept and the slope mean in that context.

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  • aqualine tree style avatar for user ojinkins
    Why is this problem in the practice? Shouldn't khanacademy keep their practice problems separate from the problems Sal does in the videos? It doesn't help anyone learn to put in the answer to a problem that they've seen done in a video.
    (17 votes)
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  • starky ultimate style avatar for user Si̶ℓvεɾ Wølƒ
    how would you figure this out if you took out the 'n' ?
    (7 votes)
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  • orange juice squid orange style avatar for user Samrita Murthy
    What is a function? What does the term, "as a function of" mean?
    (2 votes)
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  • aqualine ultimate style avatar for user sugarkin246
    From to , I didn't understand what the purpose of the function was in this problem. I thought that a function was something that describes a relationship between the input and the output, but this video didn't really make it clear what our input and output was. Was zero supposed to be our function? If so, why didn't we multiply the variable "W" by zero also, and not just on one side of the equation? I understood most of what he said other than this, so help would be appreciated!
    (3 votes)
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  • aqualine sapling style avatar for user Justin Kim
    W(n) is equal to W - 0.05(n). However, W(n) seems like W times n, not W minus a product of n. Could someone explain the meaning of W(n), and how it relates to the other side of the equation?
    (2 votes)
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    • hopper cool style avatar for user Stanley Z.
      Did you mean W(n)=32-0.05n? W(n) is read “W of n” not W times n. W(n) is really just y except it is in function notation where n is the independent variable or domain. This follows the same concept as other commonly used function notations: f(x), g(x), h(x), etc (if you’ve seen them before). All those are just another thing for y. I hope that helps :)
      (3 votes)
  • aqualine ultimate style avatar for user erica161067
    ok so it equels 0.05 ! so confusing :/
    (2 votes)
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  • leafers tree style avatar for user Leikr
    When would we ever use this?
    (2 votes)
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  • male robot hal style avatar for user rgarg99
    How does this help us with figuring out other word problems, this video only addresses this one.
    (1 vote)
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    • stelly blue style avatar for user Kim Seidel
      The concepts taught in this video apply to other word problems. In this situation, you were given the equation. The words describe the equation / function.
      1) You should read the problem as many times as needed to makes sure you understand what the function creates and what its input value represents.
      2) You should also notice that the equation is in slope-intercept form. So, you can identify the slope and the y-intercept. You should take some time to think thru what that information means in the context of the problem.
      3) The questions are tied to asking you for the slope and the y-intercept, but they are done by using info specific to the problem rather than asking you for that info explicitly.

      Hope this helps.
      (2 votes)
  • male robot johnny style avatar for user Eddy Gallegos
    sorry, why does the 0.05n cancel out when volue of water is equall to 0?
    (1 vote)
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  • blobby green style avatar for user kmperero101
    Why are word problems so hard?
    (1 vote)
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Video transcript

- Andrei has a glass tank. First, he wants to put some marbles in it, all of the same volume. Then, he wants to fill the tank with water until it's completely full. This is the formula for the volume of water Andrei should use W, measured in liters, as a function of the number of marbles used n. And we see that the amount of water he needs to put in as a function of the marbles used, n, is equal to 32 minus 0.05n. That's interesting. Complete the following sentences with the appropriate missing values. The glass tank's volume is blank liters. The volume of each marble is blank liters. So, one thing that we could do to think about the glass tank's volume is, is well, let's use this function to figure out how much water would we need if we had no marbles in it, because that amount of water would be the volume of the entire tank. Remember, we're gonna fill up the entire tank with water based on how many marbles are in it, but if we figure out what W of zero is, this is the amount of water we need if we had no marbles. This would be the volume of the entire tank and what is this going to be? Well W of zero, when n is equal to zero, this term goes away and we're left with 32. So, W of zero would be volume of entire tank. Volume of tank, which is equal to 32 liters and so, we could write 32 right over there. And then they ask us, the volume of each marble is blank liters. Well, what's going on here in this function definition? So, the highest that this could be is 32, 'cause that's the most water you would put in. If you had no marbles, you would just fill up the tank and put in 32 liters. Then, every marble that you put in, you're going to have to put in 0.05 less liters. You see that, you have minus 0.05 times n. So, every time n grows by one, you have to put in 0.05 less fewer liters of water, which implies that the marble is 0.05 liters. That's it's volume, so let's write that down, 0.05 liters. And, you could test this assumption. If you said, look, if you had one marble, if you had one marble, then you would have to put 0.05 less than 32 liters in and why would that be the case? Well, that would mean because that one marble is taking up 0.05 liters, that's how much space it's taking up.