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## Algebra (all content)

### Course: Algebra (all content) > Unit 3

Lesson 11: Interpreting linear functions and equations- Linear equations word problems: earnings
- Linear equations word problems: volcano
- Linear equations word problems: tables
- Linear graphs word problems
- Linear graphs word problem: cats
- Linear equations word problems: graphs
- Linear equations word problem: marbles
- Linear equations word problem: file transfer
- Linear equations word problems

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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.

## Want to join the conversation?

- 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)
- It helps me because I get to walk through the steps with Sal instead of us doing different problems. It helps me understand the skill better. I then take those steps that I did with Sal and apply them to another problem to help me learn how to do any problem within a certain concept.(8 votes)

- how would you figure this out if you took out the 'n' ?(7 votes)
- What is a function? What does the term, "as a function of" mean?(2 votes)
- A function is a relationship between an input and an output where each unique input value relates to only one output value.

"as a function of x" means that the function is defined for the input value "x".

Hope this helps.(4 votes)

- From0:44to1:03, 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)
- 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)
- 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)

- ok so it equels 0.05 ! so confusing :/(2 votes)
- When would we ever use this?(2 votes)
- How does this help us with figuring out other word problems, this video only addresses this one.(1 vote)
- 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)

- sorry, why does the 0.05n cancel out when volue of water is equall to 0?(1 vote)
- When you have w(0), everywhere you see a n, you substitute 0, so w(0) = 32 - 0.05(0) and zero times anything is zero, so you end up with 32.(2 votes)

- Why are word problems so hard?(1 vote)
- because they are worded differently, so it makes it harder. were not used to it.(2 votes)

## 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.