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## Describe a situation in which x and 12-x can be used to represent variable quantiies. List the domain for the answer.

Not sure what it means to represent variable quantities

Hi, Ellen.

It sounds like you just have to come up with a scenario that could be represented by two numbers which add to 12. And the scenario you choose would determine the domain.

For example, if two people split a dozen eggs, or someone is cutting a rope 12 feet long, there are many combinations of numbers that could add together to 12, but no numbers could be negative. In the case of the eggs, you could only use integers, because it would not make sense for each person to get a fraction of an egg. In the rope example, it could be cut into fractions of a foot.

So for the egg example, the domain would be {0, 1, 2, ... 12}

In the rope example, the domain would have to be numbers between 0 and 12, inclusive. In math terms, the domaiin would be:

< x < 12     "0 is less than or equal to x which is less than or equal to 12"

I am sure that you can now put your creativity to work and come up with your own situation!

Just think of it as something that can assume a range of values.

For example, if I had \$1,000 in the bank and I took home \$700 a week, an equation to represent this would be: M = 1,000 + 700*W.  Where M is money, W is week.  Both M and W would be variable quantities.