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## Algebra 1

### Course: Algebra 1>Unit 3

Lesson 2: Appropriate units

# Defining appropriate quantities for modeling

Examples for different ways to define how quantities of interest are calculated in a modeling problem.

## Want to join the conversation?

• this still confusing and I STILL NEED HELP PLEASE
• If you can identify the outputs and inputs and if you can do divisions you’re done. You just have get good at identifying input and outputs. Then divide input by output
• I always get the second question wrong.
How do i know if they're the same or they're opposite? It's really confusing.
Thanks :)
• Try extending the table on your own by just multiplying and dividing a bunch of values. It saves you time and tedium, and isn’t that much work because there are only two different tables.
• man I did some of the equations ahead and I am not getting any of it. hope ya'll are doing better
• I understand.
Sal usually does a great job but he didn't explain this very well.

When you calculate you definitions it can be confusing to find if one produces (for example) more content per writer.
Let show an example:
The question is to find which website produces more content per writer.
You find your definitions on how to figure it first.
1) Posts divided by writers
2) Words divided per writer
(This is after calculation)

Website A:
22 posts per writer
And 2,200 words per writer
(100 words per post divided by number of posts (22) )
That is Website A's content per writer.

Website B:
18 posts per writer
3,060 words per writer
That is Website B's content per writer.

At first glance you'd probably like to say that B has more content, right?
But you must compare both A and B's posts and words per writer.
Posts per writer: [ A = 22 ~ B = 18 ]

Words per writer: [ A = 2,200 ~ B = 3,060 ]
'B' has more words per writer.

This means they have opposite results.
Why?
But 'B' has more words per writer. So they have opposite results.

Now, if they both had 22 posts per W but the words per W stayed the same, only then you could conclude that B had more content.
Does that help or make any sense? I hope so :)
• Please explain why we call this idea
"Defining Appropriate Quantities for Modeling".
What specifically does that mean? Where are the models? Why do we say "define" instead of find? Why isn't this subject named "How to analyze & compare information from tables"? I understand why they put "appropriate", though. I think it was because in these problems we always have to decide which data is more relevant.
• how would you know what is an input or an output?
• It is generally agreed that an input is what you are putting into the thing that you are creating, e.g kilograms of metal bought, and an output is what you get because of it, e.g profit from cars sold.

Hope this helped!
• If your confused, don't feel alone, because literally everyone who commented here is also confused.
• yeah but its really getting on my nerves. He isnt explaining it properly. Its super annoying
• For the first question, why can't it be area/volume instead of volume/area?
• It seems both are technically correct and that it is a matter of convention. You are forced to use your unit together with other established units, so if the other units use this kind of convention then if you use area/volume you wouldn't be able to simplify it with the other units. In real world practice I think you should use whichever helps you figure out and solve the problem at hand the easiest. There seems to be a subtle difference between fractions and units, which has to deal with conversion of units, since 1/10 =/= 10/1, but, 1 meter / 10 seconds = 10 seconds / 1 meter, so, that is something to think about.
• How do I know if I should add inputs with inputs or multiply inputs by inputs?
• In defining appropriate quantities for modeling, whether to add inputs with inputs or multiply inputs by inputs depends on the specific situation and the relationship between the inputs.
If the inputs are independent and do not affect each other, then they can be added together. For example, if you are modeling the cost of a meal at a restaurant, you might add together the cost of the entree, the cost of the drink, and the cost of the dessert.
If the inputs are related and affect each other, then they should be multiplied together. For example, if you are modeling the distance traveled by a car, you might multiply the speed of the car by the time it has been traveling.
It is important to carefully consider the relationship between the inputs and the desired output when defining appropriate quantities for modeling. In some cases, a combination of addition and multiplication may be necessary.
In summary, whether to add inputs with inputs or multiply inputs by inputs in defining appropriate quantities for modeling depends on the specific situation and the relationship between the inputs.