Math (Can Someone Please Help Me Work Through This)

[ImagineDragons]

For the table, identify the independent and
dependent variables, Represent the relationship
using words, an equation and a graph.


# of cases of | # of bottles
bottled | of water, b
water, c |

1 | 24
2 | 48
5 | 120
10 | 240
20 | 480

So in this case I think the independent variable would be C (the number of cases of bottled water) and the dependent variable would be B (the number of bottles of water), because the amount of bottles of water depends on how many cases there are.

And so every case has 24 bottles of water, so the equation somehow needs to connect the two... can someone please help explain to me how I would write the rest of the equation?

[Buenchico]

b = 24c

[Old_Geezer]

That seemed too obvious to me. Can't be the answer.

[ImagineDragons]

That's why I'm not sure, sounds too simple to be true

[bhg481]

I think the answer is as obvious as Buenchico has written, OG. Since the question requires 3 parts to its answer he also needs words to the effect of "The number of bottles is twenty-four times the number of cases" and a straight-line graph, "c" along the X axis, "b" up the Y axis, through the origin and the point 20 480.

[New Judge]

Just the one math, is it?

[bhg481]

He probably lives in the colonies NJ.

[Buenchico]

>>> sounds too simple to be true

I did look at it several times, just to check that I'd not missed something. However I'm confident that it's the only answer that fits the data.

(I've got a university degree in mathematics, and taught it up to university entrance level, BTW)

[Mamyalynne]

We reach all corners of the globe.

[ImagineDragons]

And then for the graph I would put c on the x axis and b on the y, and then what?

[bhg481]

and then draw a straight from the origin to the point 20,480

[Buenchico]

^^^ If you're confused by NewJudge's post, ImagineDragons, it's because this website is based in the UK, where 'mathematics' is always shortened to 'maths'. The use of 'math' in your question (which sounds totally wrong to us) suggests that you're in the USA.

[ImagineDragons]

What do you mean?

[bhg481]

In Britain we call the point 0,0 the origin.

[Baldric]

https://www.muncysd.org/cms/lib7/PA06000076/Centricity/Domain/75/Section%204-2%20Patterns%20and%20Linear%20Functions.pdf

[zebo]

Label the axes b and c on the x and y axes respectively. Plot (0,0) and (24,1), join them together with a straight line.

[Buenchico]

^^^ Bhg481 means that you need to scale your graph so that the horizontal axis goes from 0 to 20, with the vertical one going from 0 to 480. Then (since 0 cases hold 0 bottles), join the origin (0,0) to (20,480).

[ImagineDragons]

B is the dependent and c is the independent right?

[New Judge]

But looking at independent and dependent variables as “cause and effect” the relationship in this instance can be viewed either way. It is quite true to say that the amount of bottles of water depends on how many cases there are. But it’s equally true to say that the number of cases depends on the number of bottles. If you are asked “How many cases are there?” the answer is “Bottles/24”. If you are asked “How many bottles are there?” the answer is “Cases*24”. It depends what is being varied, the cases or the bottles.

If the question is “The factory produces x number of bottles in a day, how many cases is that?” then the formula is x/24. The cases are dependent on the bottles. If the question is “The factory must produce x number of cases per day, how many bottles must it produce?” then the formula is x*24. The bottles are dependent on the cases.

The direction of the dependence” is defined by what is varied, the cases or the bottles and we have not been told. The formula (and a graphical representation) is simple. Which of the two is the dependent variable and which is the independent variable is unknown because we are not told.

[ImagineDragons]

Ok, thank you everyone SO MUCH

[bhg481]

I woke up this morning and wondered if we had been slightly miskeading you about the graph. As experienced people we all spotted that it would be a straight-line graph; as a student you would not necessarily spot that. What you have to do is to draw a graph with b along the x-axis and c up the y-axis. You then plot every point on the graph ie, (1,24), (2,48) etc and then look to see what sort of line you can connect them with. You will see that it is a straight line, which happens to go through the origin because zero cases contain zero bottles. Straight lines fit the equation y=mx+c, and you will be able to see from your graph that the gradient m = 20 and c=0 because the line goes through the origin. This will enable you to read off the graph how many bottles (say) 3.5 cases will contain or calculate it by substuting in the formula now that you have acquired m abd c from the graph.
The "words" you require to answer the question will be of the form "The number of bottles is directly proportional to the number of cases".